Mathematics - 2014-03-03 (page 3 of 4)

Pedro Tamaroff

4:04 PM

HAI MAIK

@mike

Im watching pacificvrim

Sawarnik

4:34 PM

@PedroTamaroff Silly movie.

@BalarkaSen Is your appointment over? When it is?

r9m

@Sawarnik Not just silly ... bogus with a capital B :P

agent154

I'm having a terrible time visualizing this problem. Can anybody offer any insight?

A national singing contest has five distinct entrants from each state. Use a generating function for modeling the number of ways to pick $20$ semifinalists if there are at most three people from each state.

I want to say that I need to solve $e_{1}+e_{2}+e_{3}+\cdots+e_{50}=20$ where $0\leq e_i\leq 3$, but then I feel like i'm not counting some of the contestants.

If I go with that, I'd have $(1+x+x^2+x^3)^{50}=20$

But the contestants are distinct, not the same.

Matt N.

5:51 PM

Hullo.

Jasper Loy

@MattN. Hi! Hope you are doing well.

Matt N.

@JasperLoy Hi there. Well, not too bad I guess. Got a broken knee and sinusitis and hay fever but otherwise I'm good. What about you? Making any progress with that OCD?

Balarka Sen

@Sawarnik Yes, but I have another tomorrow.

Jasper Loy

@MattN. Hmm, trying to, trying to...

Matt N.

I don't know but on chat you seem pretty normal. Is it really that bad?

Balarka Sen

5:53 PM

The sum'll come out... tomorrow... betchcha bottom!

Jasper Loy

@MattN. Yes, I dare not say the number of years I have not worked.

Balarka Sen

Talk to you later, byes!

Jasper Loy

Why star all the nah's?

Matt N.

@JasperLoy Yes but was there really no way you could have? I notice with my knee that I don't do certain things that I could probably do.

@JasperLoy I have no idea.

"nah" is way after my (SE-)time.

Jasper Loy

@MattN. Maybe I could have, but I don't have the confidence. A few times I did try to find some work, but it got worse.

Matt N.

5:55 PM

@JasperLoy Maybe the wrong work?

Jasper Loy

Anyway, I hope to be well enough to start studying soon, I still hope to go to grad school.

Matt N.

But anyway, I'm not here to advise you. You'll know best.

Sure.

Jasper Loy

Well, there are people who are debilitated their whole lives from mental illness, so it's scary.

Matt N.

Yes.

Jasper Loy

Nash took twenty years to recover from his schizophrenia.

But at least he proved the Nash embedding theorem, I have proven nothing, lol.

Matt N.

5:57 PM

You still may : )

Jasper Loy

Yeah, maybe one of the millennium problems, haha.

Matt N.

You can either come up with the famous Loy conjecture or alternatively state and prove the Loy theorem.

Jasper Loy

Same for you, the N. conjecture or the N. theorem.

Matt N.

We'll see.

I'm actually aiming much lower.

Jasper Loy

Have you decided on your speciality topic?

Matt N.

5:59 PM

Just want to be a lecturer and have enough free time to work on stuff.

No, actually I find this decision impossible to make.

Jasper Loy

Yeah, everything seems so interesting.

Matt N.

Exactly.

Jasper Loy

Maybe choose what you are best at.

Matt N.

It'll be a more important topic once I decide on a PhD. For the MSc's I guess it's not really all that important.

I've been wondering though about how you can make the optimal choice for a PhD supervisor.

Jasper Loy

Yeah, in fact I never understood why they make people write theses for the BA and the MA.

Matt N.

6:02 PM

To learn how to write a thesis. Obviously : )

There's enough other stuff to learn during your PhD I suppose.

Jasper Loy

I think at the lower levels it is more important to take courses as there is so much to learn.

Matt N.

Also true.

This conversation is too serious.

Jasper Loy

Anyway, I had to write something for my BA, which I did.

Matt N.

Which subject?

Jasper Loy

I wrote something about Lebesgue integration in R^n.

It was an uncommon approach that in the end turns out to be equivalent to the usual one.

Matt N.

6:04 PM

Measure theory. Nice.

Caipiranha!

Do you drink?

Jasper Loy

Nope, only occasionally.

I don't smoke at all.

Matt N.

Me neither.

It makes no sense.

But drinking does: it's a kind of blissful state you reach.

Jasper Loy

How about drugs? I don't do drugs, lol.

Matt N.

I don't either. But if someone gave me a packet of amphetamines I'd take it!

For sure.

Jasper Loy

The panelty for drug trafficking here could be death.

@mike I did a google and am trying to figure out which image is yours, lol.

Hey @seaturtles, how is school?

sea turtles

6:14 PM

meh

Jasper Loy

Meh is one of your fave words.

sea turtles

hmm, the starboard is interesting this morning

Jasper Loy

Yes, but so far all wrong. I will write the correct version, remember to star it.

Nah.

Nobody is starring it, sad panda.

Matt N.

Starred.

Sorry, was afk. Had to get dinner going.

I feel like I'm turning into a cook.

Thinking about signing up for cooking classes.

Crickets.

Pedro Tamaroff

►

HAI @MattN. @seaturtles

Matt N.

6:29 PM

Tumeni videos.

Pedro Tamaroff

Tumeni. \loves

Matt N.

@PedroTamaroff HAI = Hello awesome internetters?

Hai = yes in Japanese.

Pedro Tamaroff

Yes, this is dog.

Matt N.

Yo, dawg, wassup?

Ooooh, this makes me miss Trevor Phillips and the gang.

</3

GTA 5 was way too short.

Pedro Tamaroff

Never played that one.

=D

I ended up in Vice City.

Matt N.

6:33 PM

Never played any of the other GTAs.

Pedro Tamaroff

WAT.

Matt N.

True story.

Pedro Tamaroff

@MattN. You should play Vice City.

Matt N.

I used to be a Nintendo person. More or less. And I don't think there are any GTAs on Nintendo devices.

Pedro Tamaroff

@MattN. YAY. I have SNES.

Still working.

Have my Super Mario World.

Matt N.

6:35 PM

@PedroTamaroff And you should get GTA 5 and get to know Trevor Phillips. : D

@PedroTamaroff Poor me. I don't have mine anymore because it was lost when I moved once.

Sad.

Nor do I have my 80ies Game Boy.

Even sadder.

Complex analysis

@MattN. hi there

Matt N.

Change of topic this is too sad.

@Complexanalysis Hello

Complex analysis

what have you been upto ? @MattN.

Matt N.

@Complexanalysis Nothing. What about you?

Complex analysis

trying to read some measure theory @MattN.

Matt N.

6:37 PM

Do you have a book or is it lecture notes?

@PedroTamaroff Actually, I think I'll rename my account to Trevor Phillips.

Complex analysis

@MattN. wikipedia :P

Matt N.

The sound track is also wicked. Let me show you.

@Complexanalysis : )

@PedroTamaroff e.g. Me gusta : )

Pedro Tamaroff

"The Black Angels".

Matt N.

Especially if you listen to it while you are speeding, running over motorbikes and being chased by police : D

@PedroTamaroff You know it?

Pedro Tamaroff

@MattN. Nope. Just translatin'.

Matt N.

6:40 PM

The king and I.

Jessy Cat

@JasperLoy, I know how you feel.

Complex analysis

@MattN. Prove $$\sum_{n,m= 1}^{\infty} x_{nm} =\sum_{n=1}^{\infty} \sum_{m=1}^{\infty} x_{nm} =\sum_{m=1}^{\infty} \sum_{n=1}^{\infty} x_{nm}$$ for $x_{\alpha} \ge 0$ .

Matt N.

@PedroTamaroff or this.

@Complexanalysis Gimme a minute need to get mathjax up and running.

Pedro Tamaroff

@Complexanalysis Do you need help with that?

Complex analysis

@PedroTamaroff Sure :-)

Pedro Tamaroff

6:45 PM

@Complexanalysis Sure you need help?

So, the important thing to observe is we want to work with $\sup$s.

Complex analysis

@PedroTamaroff Sure sure :D

Pedro Tamaroff

OK.

Complex analysis

@PedroTamaroff lets go !

Pedro Tamaroff

So, we can prove that $$\sum_{i\geqslant 1} \sum_{j\geqslant 1}x_{ij}=\sum_{i,j\geqslant 1}x_{ij}$$

And the other part follows by symmetry.

Agreed?

Matt N.

W00t. I did it. Now for the sums.

Pedro Tamaroff

6:48 PM

?

Matt N.

Oh, Pedro is at it. Okay : )

I'll bbl.

Pedro Tamaroff

@MattN. Sorry, did you want to do it?

Matt N.

No, too drunk. Just want to sit and drink more.

bbl

Pedro Tamaroff

@Complexanalysis

OK.

So, note that $$S=\sum_{i,j\geqslant 1}x_{ij}=\sup \left\{\sum_{(i,j)\in F}x_{ij}:F\subseteq \Bbb N^2\text{ finite }\right\}$$

Complex analysis

@PedroTamaroff We might be able to prove the first equality , but how

Pedro Tamaroff

6:53 PM

In a similar fashion, $$b_j=\sum_{i\geqslant 1}x_{ij}=\sup\left\{\sum_{i\in F_j}x_{ij}:F_j\subseteq \Bbb N\text{ finite }\right\}$$

Complex analysis

@PedroTamaroff How can you say that there is $S$ such that the first equality holds ? Putting it other way , you are telling me that $\sum_{i,j} x_{ij}$ is defined as the $\sup$ over the finite indexing set .

Pedro Tamaroff

@Complexanalysis Aha.

That's how one defines that sum.

Complex analysis

@PedroTamaroff What do you mean by Aha ? just to get your expression right :-)

Pedro Tamaroff

That's what I'm saying.

Or you can prove it equals that.

Whenever $x_{ij}\geqslant 0$.

@Complexanalysis Aha = Nod.

So, by the above, note that for each $j$; $$ \sum_{j\geqslant 1}x_{ij}\leqslant \sum_{i,j\geqslant 1}x_{ij}$$

So, $$\sum_{i\geqslant 1} \sum_{j\geqslant 1}x_{ij}\leqslant \sum_{i,j\geqslant 1}x_{ij}$$

Complex analysis

@PedroTamaroff Okay , i think i can prove that breaking it into two cases , ie when the sum is divergent and when the sum is convergent and arguing that there exists $(N,M) \ge (n,m) \in \mathbb N \times \mathbb N $$\ for every $\epsilon > 0$

Pedro Tamaroff

6:58 PM

@Complexanalysis So, what you should aim to show is that for each $\varepsilon >0$; you can make $$\sum_{i\geqslant 1} \sum_{j\geqslant 1}x_{ij}\geqslant \sum_{i,j\geqslant 1}x_{ij}-\varepsilon$$

Complex analysis

ya @PedroTamaroff

Balarka Sen

@Sawarnik There?

Complex analysis

how do you define $\sum_{j \ge 1} x_{ij}$?

Okay ok , i got it . @PedroTamaroff just got confused with the notations .

Pedro Tamaroff

@Complexanalysis Good.

Sorry, I was diverted a second.

@Complexanalysis Maybe you can read this and ask me?

N3buchadnezzar

Heya

Balarka Sen

7:09 PM

Hullo

Complex analysis

@PedroTamaroff ya i got it , next step i want to know is when can i extend this theorem for a sequence even with the negative terms ?

Balarka Sen

@N3buchadnezzar Have you learned PNT?

Pedro Tamaroff

@Complexanalysis No, you can't.

Negative stuff fucks things up.

But, you can do it when the sum converges absolutely.

Tonelli's theorem.

Complex analysis

@PedroTamaroff if the sum converges absolutely then the Tonelli theorem holds again.

Pedro Tamaroff

@Complexanalysis Yiss.

Do you know a little measure theory?

Balarka Sen

7:17 PM

@PedroTamaroff Yiss Preciousess.

Complex analysis

@PedroTamaroff nothing apart from some definition . I like it though .

Pedro Tamaroff

It's a really nice subject.

N3buchadnezzar

@BalarkaSen Prime number theorem yeah?

Balarka Sen

And you still haven't linked me to that Katsumura paper...

Pedro Tamaroff

I haven't studied it much, just a tiny bit.

Complex analysis

7:18 PM

@PedroTamaroff Do you know it well ?

N3buchadnezzar

We have been using two weeks now learning the basics to understand the proof

Complex analysis

@PedroTamaroff How much have you learnt ?

Balarka Sen

@N3buchadnezzar Are you gonna go Selberg? Or the other way, i.e., no $\zeta$ zero on 1-line?

Pedro Tamaroff

@Complexanalysis Well, a decent amount from one viewpoint. I read Shilov's book "Integral, Measure and Derivative."

N3buchadnezzar

@BalarkaSen Both

Balarka Sen

7:20 PM

Cool and good.

Pedro Tamaroff

@BalarkaSen Here you go.

Balarka Sen

@PedroTamaroff Not seeing vids from ytubes.

Complex analysis

@PedroTamaroff How is the book ?

Balarka Sen

they can make you EVIL!!

N3buchadnezzar

@BalarkaSen 'i have read the outline of both proofs they seem still somewhat heavy

Balarka Sen

7:21 PM

@N3buchadnezzar Yeah, those heavy guns.

But I like the 1-line proof very much.

You should first go through Merten's theorem.

N3buchadnezzar

nah

Balarka Sen

Here we go.

Pedro Tamaroff

@Complexanalysis It's pretty nice.

@BalarkaSen You do realize it was all just a joke, right?

Balarka Sen

What book, @N3bu?

@PedroTamaroff I realized alright, but a bit later. =P

As you might have guessed.

N3buchadnezzar

apostol

Balarka Sen

7:23 PM

@N3buchadnezzar Nice one. What have you covered up until now?

N3buchadnezzar

up to 11

skipping quadratic residues and that

Balarka Sen

I don't have a copy myself (not now, at any rate) and I never read Apostol throughly (my ideal is I&K) so I don't know what 11 has on it.

@N3buchadnezzar OMG, don't do that!

You'll need characters and what-nots

In L-theory

Complex analysis

@PedroTamaroff I am trying to go through Terry tao's book .

lecture notes to be precise

Pedro Tamaroff

@Complexanalysis Don't know that one.

Balarka Sen

@Complexanalysis In Measure theory?

I don't know of one.

Pedro Tamaroff

7:26 PM

They say Folland is a good book.

I started reading it.

Balarka Sen

@Pedro Recommend a book in alg topo.

I figured I don't like the diff geo POV

Complex analysis

Ok . @PedroTamaroff

Pedro Tamaroff

@BalarkaSen Hatcher is "The Book"; apparently.

Balarka Sen

@PedroTamaroff Okay, so I need a bit Homo and Cohomo from D&F, right?

Complex analysis

@PedroTamaroff ya , Hatcher is supposed to be the main book .

Pedro Tamaroff

7:28 PM

But you cannot expect to read that one if you don't know topology. I guess.

Balarka Sen

@PedroTamaroff I am learning the basics.

But I don't believe that much DGPOV is really nessesary for alg topo, is it?

Pedro Tamaroff

@BalarkaSen What the hell is DGPOV.

Balarka Sen

Differential Geometric Point Of View

Pedro Tamaroff

You need to know topology.

Balarka Sen

I know, but do you need differential geometry to approach topology thoroughly?

You know, people say one can attack it through algebra.

Just like the way we approach NT from PT, you know.

Pedro Tamaroff

7:32 PM

I don't think so.

But you can read Spivak's Calculus on Manifolds for a first start on Diff. Geo.

Balarka Sen

Spivak got a Calc, that I knew, but Calc on Mani?

I didn't know that.

Pedro Tamaroff

Yes.

Balarka Sen

But wouldn't it be a lot off-the-tangent for me to dive on Diff. Geo.?

Complex analysis

@PedroTamaroff Do you know what is the problem with the jordan measure which makes us to go for lesbegue measure ?

Balarka Sen

I mean, I like NT. Especially ANT and TNT.

Pedro Tamaroff

7:35 PM

@Complexanalysis It isn't a measure to start with. =D

IIRC it is not countably additive.

N3buchadnezzar

@BalarkaSen Oh it it just all of us has already had number theory

Complex analysis

@PedroTamaroff What is IIRC ?

N3buchadnezzar

We have learned a bunch about L functions and Dirichlet Characters

Balarka Sen

@N3buchadnezzar That's fine then.

What have you learned on field theory?

N3buchadnezzar

I have taken an introductory course in Algebra

but alas do not remember much from it

Balarka Sen

7:37 PM

Field theory is important in learning L-automorphs.

Pedro Tamaroff

@BalarkaSen I just think you need to learn a few more basics things before launching up.

Balarka Sen

Had anything on algebraic geometry?

@PedroTamaroff Ineqs perhaps, but that's just if I ever learn topology.

I really hate inequalities. Even diophantine approximation of TNT because of that.

N3buchadnezzar

Heh taking complx analysis and topology along with ant

Balarka Sen

CA is good.

And important.

Alas I think I will never grasp topology.

Pedro Tamaroff

@BalarkaSen WAT.

N3buchadnezzar

7:41 PM

@BalarkaSen ヽ༼ຈل͜ຈ༽ﾉ Are you not HAUSDORFF enough? ヽ༼ຈل͜ຈ༽ﾉ

Balarka Sen

@Pedro Someone told me that there are number theoretic approaches on learning topology. Do you think it's true?

Pedro Tamaroff

@BalarkaSen No.

Balarka Sen

@PedroTamaroff Odd. A topologist (professional, yes) himself said so.

@PedroTamaroff WYSIWIS

Pedro Tamaroff

@BalarkaSen Well, you asked for my opinion. Just pick a topology book and read it. And if you don't understand it read it again.

=)

Balarka Sen

One in a million opinion =)

Dang my internet connection.

@PedroTamaroff He says perspective matters. I wonder what that means ...

N3buchadnezzar

7:45 PM

@BalarkaSen You should read my professors notes, they are very elementary

Pedro Tamaroff

@BalarkaSen I wonder too.

Balarka Sen

@N3buchadnezzar nah

N3buchadnezzar

nah

Balarka Sen

@PedroTamaroff His name is Mahan Mitra, you can google him on the internet. I don't understand any of his works however.

N3buchadnezzar

what does even opinions mean?

Balarka Sen

7:48 PM

I just wonder why $\text{PSL}(2, \Bbb{C})$ pops out everywhere.

Anthony

Anyone good with gradients?

Dipole

In physics, there are several kinds of dipole: *An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some (usually small) distance. A permanent electric dipole is called an electret. *A magnetic dipole is a closed circulation of electric current. A simple example of this is a single loop of wire with some constant current through it. *A current dipole is a current from a sink of current to a source of current within a (usually conducting) medium. Current dipoles a...

How did they get the field?

Pedro Tamaroff

So, I am trying to find an involution in ${\rm SL}(2,5)$.

Complex analysis

@PedroTamaroff what is involution ?

Pedro Tamaroff

@Complexanalysis An element for which $x^2=1$.

It is sometimes confused for an idempotent, which is an element for which $x^2=x$.

=)

Complex analysis

@PedroTamaroff $A\in F^{n \times n} $ such that $A^2=I$ ?

Pedro Tamaroff

8:01 PM

No. Matrices in $\Bbb Z_5^2$ with $A^2=1$ and $\det A=1$. =D

In general ${\rm SL}(n,k)$ is the group of $n\times n$ matrices over the field with $k$ elts with determinant $1$.

Complex analysis

Yup .

Paul Epstein

Hello everybody

Pedro Tamaroff

@Complexanalysis So $$\begin{pmatrix}-1&0\\0&-1\end{pmatrix}$$ does the job.

Paul Epstein

Is Mike in?

Pedro Tamaroff

I have to prove this involution is unique.

@Mike just entered.

Paul Epstein

8:04 PM

I should say @Mike, I suppose.

N3buchadnezzar

ヽ༼ຈل͜ຈ༽ﾉ

Mike

@Pedro Unique up to what?

Complex analysis

looking for $a, b , c, d$ such that $ad-bc =1$ ?

Pedro Tamaroff

@Complexanalysis And four more equations, over $\Bbb Z_5$.

@Mike Unique.

Just that.

Paul Epstein

@Complexanalysis Not such a hard find. Looking to make ad-bc = 1 is a bit easier then looking for ways to reduce global warming.

Mike

8:06 PM

Well that ain't true.

Paul Epstein

@Mike, Sorry I'm probably out of context here.

Pedro Tamaroff

@Mike ORLY.

Paul Epstein

There is probably a context where making the det 1 is difficult.

Pedro Tamaroff

Well then Rotman is pulling me legs.

Paul Epstein

@Pedro what does ORLY mean?

Mike

8:07 PM

@Pedro How did you define involuntion?

Pedro Tamaroff

@Mike $x^2=1$, $x\neq 1$, I guess.

Mike

Ah, okay. I didn't see the second part earlier. :D

Paul Epstein

@Mike, what's your grad school news?

Mike

nada

Paul Epstein

@Mike, here's the difference in a nutshell between a career in the corporate world and a career in academia. In academic life, the main determinant of your future is how well you do. In corporate life, the main determinant is how well the company does. If a mathematician is working in industry, then if the company is doomed, the job is doomed even if the mathematician is a Fields medallist. If the mathematician is working in academia, then even if the dept. is not highly ranked

the mathematician will do well if good results are forthcoming.

Perhaps the above is trite and banal, but to me it's a crucial distinction.

Pedro Tamaroff

8:21 PM

@Mike So yeah, the system is easy to solve.

Skovy

Hello

How to I convert a plane in Cartesian coordinates (z=k) into spherical coordinates? (p=?)

Pedro Tamaroff

@Mike I think I got it.

Complex analysis

@PedroTamaroff what did you get ?

Pedro Tamaroff

@Complexanalysis I have to show that the quarternions are iso to the $2$-Sylows of ${\rm SL}(2,5)$.

Complex analysis

@PedroTamaroff the order of $SL(2,5)$ is ? half of $GL(2,5)$ ?

Pedro Tamaroff

8:36 PM

@Complexanalysis No, a fourth.

Because $5-1=4$.

In general ${\rm GL}(n,k)=(k-1){\rm SL}(n,k)$.

Reason Use the determinant map $\to F^{\times}$ that has size $k-1$.

Complex analysis

No i don't get , SL is group with determinant 1 and GLN is group with det $-1, 1$ right ? @PedroTamaroff

Pedro Tamaroff

@Complexanalysis No.

$ \rm GL$ is all invertible matrices.

Complex analysis

@PedroTamaroff Oh oh , i got it . I got confused with the Orthogonal group .

Pedro Tamaroff

SIGH I cannot make W|A compute matrices mod 5.

Pedro Tamaroff

9:02 PM

@DanielFischer

How can I show a $2$-Sylow of ${\rm SL}(2,5)$ cannot be abelian?

Or cyclic.

I have shown a $2$-Sylow of that has a unique element of order $2$.

Daniel Fischer

@PedroTamaroff $SL(2,5)$ is the $2\times 2$ matrices over $\mathbb{F}_5$ with determinant $1$?

Pedro Tamaroff

The groups of order $8$ are $D_8,Q_8,C_8,C_2\times C_4,C_2^3$. Thus, I am left with $Q_8$ or $C_8$.

@DanielFischer Yes.

I have found elements in $SL(2,5)$ with $x^2=-1$, but wasn't able to find $Q_8$ inside it =P

Even noncommuting elts with $x^2=y^2=-1$.

But they were bad noncommuting.

I need $[x,y]=-1$ too.

Daniel Fischer

@PedroTamaroff If nothing else helps, brute force will, $SL(2,5)$ isn't large ;)

Pedro Tamaroff

@DanielFischer Heh, $120$ elts is big enough for me. =D

I am trying to see if I can show the $2$-Sylow isn't cyclic.

Thus, I have to show it is not abelian.

Because it already has a unique element of order $2$.

During by search, I learned $SL(2,5)$ is one of the three unique nonsolvable IC groups.

Daniel Fischer

@PedroTamaroff Don't $$\begin{pmatrix}2&0\\0&3\end{pmatrix};\quad \begin{pmatrix}0&4\\1&0\end{pmatrix}$$ do the desired?

Pedro Tamaroff

9:10 PM

@DanielFischer I didn't come across those. =P

I tried $\begin{pmatrix}2&0\\0&-2\end{pmatrix}$, $\begin{pmatrix}2&0\\1&-2\end{pmatrix}$,$\begin{pmatrix}2&1\\0&-2\end{pmatrix}$, $\begin{pmatrix}3&0\\1&-3\end{pmatrix}$... among others.

@DanielFischer They do. I'm so jealous =D

Daniel Fischer

XD

Pedro Tamaroff

@DanielFischer Wait.

@DanielFischer How did you find them?

Daniel Fischer

$$\begin{pmatrix}i&0\\0&-i\end{pmatrix};\quad\begin{pmatrix}0&-1\\1&0\end{pmatrix}‌$$

$i\leadsto 2$

Pedro Tamaroff

@DanielFischer Ah, right. =)

Now I have to show $A_4$ doesn't embed in $SL(2,5)$.

Complex analysis

@DanielFischer grrreat :D

Pedro Tamaroff

9:20 PM

@DanielFischer That proves $S_5\not\simeq {\rm SL}(2,5)$, since $D_8$ is a $2$-Sylow of $S_5$.

Daniel Fischer

Yep. Regarding $A_4$, does $Q_8$ contain a $V_4$?

Pedro Tamaroff

@DanielFischer No, $Q_8$ has three copies of $C_4$ and one of $C_2$.

@DanielFischer I meant $A_5$.

Sorry.

=)

Daniel Fischer

Same argument, the $2$-Sylow subgroups of $A_5$ are $V_4$.

Pedro Tamaroff

@DanielFischer $V_4\leqslant A_4\hookrightarrow A_5$.

@Mike Hello.

Mike

GRRrrnh, @Pedro

Pedro Tamaroff

9:35 PM

@Mike Yo took a nappy?

@seaturtles Hey there.

sea turtles

herro

Pedro Tamaroff

so, you prefer the sea to hot cocoa?

Mike

I have never heard I not cocoa turtles

Pedro Tamaroff

@Mike Are you high?

@robjohn

robjohn

9:50 PM

@PedroTamaroff It doesn't want to stay Pedro

Pedro Tamaroff

@robjohn How can I adjust the size of the pic here

robjohn

there

Sawarnik

@robjohn You saw my question?

I am considering a bounty on it now.

robjohn

@PedroTamaroff I don't know if SE supports IMG tags in HTML. If it doesn't, then you have to resize the image then reupload.

@Sawarnik why is it important? You're assuming the actual question was stated wrong, aren't you?

@Sawarnik maybe I am thinking of the wrong question again

Sawarnik

@robjohnI think you are thinking of the correct one. The thing its not always false, sometimes its true. Tats my question, when its true? It is not important, no simple math question is. Actually, I am considerably fascinated by the question. My attempts have failed till now. I just pinged you if had any idea. No problem :)

robjohn

9:57 PM

@Sawarnik Hang on, I will write and answer

Sawarnik

Ok.

I maybe on and off though. My exam starts in 4 hours, and I have 2 [biology] chapters to do.

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$Mathematics$ Mathematics