It's rare that I can get distracted by two separate pianos in a row

Hi @Kasmir and DogAteMy ... you're walking down a row of pianos, DogAteMy?

Ted :D

I am doing the first isomorphism theorem

I got a bit stuck

Nah.

Kinda need a dos of your wisdom :D

Hmm ._.

Can you put it in words the result of that theorem ?

Why don't you try?

well so far this is what i got

we start with surjective hom

we can allways do that ,f: G--->H, if we take only the image of f

what we do next we take the map Pi: G-->G/K

What's $K$?

K is the kernel

OK.

and another map f* : G/K ---> H

Hai

Huh? Where did that come from?

hi Demonark

what did what come from ?

$f^*$

You mean the notation is bad ? or the map is wrong

i meant f bar

just something different from f

You just said we take another map $f^*$. What is it?

Yeah, star isn't good. $\bar f$ is better.

okay should I continue ? or i did not answer yet?

$\bar f$ : G/K ---> H

You didn't answer. You just take any old $\bar f$, or is it made up using $f$ somehow?

well

$\bar f$ is an isomorphism

defined how?

By taking cosets of K

that's elements of $G/K$

Yes we start from G and we collapse the elements of G into G/H

equivalence classes

What does this have to do with $f$?

I am not sure I understand the question but , f was not 1-1

but when we collaspe G into G/H

You're supposed to define $\bar f$ for me.

ah okay

$\bar f$ : aK --> a

No.

take a coset to one representative

okay let me think

You're defining a homomorphism from $G/K$ to $H$.

but that is more than hom

One step at a time.

Okay

I was lost in notation, wrote H instead of K ( noticed that just now )

Okay let me see how to define $\bar f$

You need to read your book and study it. And this is all in my book, too, of course.

Read and study with pencil ... work out all the details for yourself (without reading the book).

I did that but maybe i need second read

am not sure what your question was tbh

you wanted me to define f bar

@TedShifrin Can I PM you in a minute? (I.E. Open up a private room)

the elements of G/K are of the from aK , a in G

OK, DogAteMy ...

So you need to know what $\bar f(aK)$ is, @Kasmir, and you need to know why (1) this is well-defined, (2) this defines a homomorphism, and (3) it is a bijection.

You need to work this all out for yourself.

aK* bK = ab K

Is that what you wanted?

No. Read what I wrote and go do it.

I ll do that now

I don't have the patience to sit here through this.

You need to prepare.

I understand that and thanks for help

Yes I know its all fuzzy with these defintions

and notation

Ill have a second read and come back

I have lots of examples in my book.

am looking at it now =p

hi chat

Hullo

hi Demonark — how're classes?