Finite Group Theory - 2014-12-18

Alexander Gruber

03:00

room topic changed to Finite Group Theory: [finite-groups]

room topic changed to Finite Group Theory: [finite-groups] [group-theory]

I won't write a long introduction. At some point, I will ping some people who post in the finite group theory tag on the main site, to let them know this is here. As a special interest chat room, it may not survive, but we will see what happens.

If you'd like to become an coowner of the room, ping me here and let me know.

room topic changed to Finite Group Theory: Let this be a place to come together and discuss finite group theory. Links to papers and interesting questions can be starred/pinned. We can also help each other with GAP. [finite-groups] [group-theory]

Pedro Tamaroff

@AlexanderGruber This is nice.

Alexander Gruber

@PedroTamaroff I'm liking it my friend!

Pedro Tamaroff

@AlexanderGruber You should post a weekly problem!

Alexander Gruber

@PedroTamaroff That's a really good idea. At the very least it would keep the room alive for a while, to let it catch on.

Pedro Tamaroff

Let's see if I can recall one, which isn't too trivial.

Here: let $G$ be a finite $p$-group. Then $\Phi(G)=G'G^p$.

Can I own dis @AlexanderGruber?

Stack Exchange

03:18

Alexander Gruber has added Pedro Tamaroff to the list of this room's owners.

Alexander Gruber

It is done.

Pedro Tamaroff

Yay.

I will post the solution to the problem posed on Monday next week.

Alexander Gruber

Weekly Problems: Discuss and post your attempts! I will sometimes offer bounties for alternative proofs, scaling with the creativity of the solution.

^ the above can be modified as this room (and its culture) develops.

Pedro Tamaroff

03:34

@AlexanderGruber Alex.

You know what always bugged me?

Alexander Gruber

@PedroTamaroff What's that?

Pedro Tamaroff

@AlexanderGruber The following theorem: a group acts primitively on a set iff the stabilizers are maximal.

I never grokked it.

Alexander Gruber

@PedroTamaroff I remember you talking about that some time ago.

Pedro Tamaroff

@AlexanderGruber Yeah, long time ago with anon.

I was reading my old notes in Rotman and Jacobson (snif, snif) and I found this. =)

I should retake Rotman's book some day. I was getting into nice discussion, like the family of simple groups ${\rm SL}(2,k)$ and the ${\rm PSL}$s.

Alexander Gruber

@PedroTamaroff I'm taking this modular rep theory course right now and we recently spent a couple days on computing all the conjugacy classes and character tables of all those linear groups.

It was pretty interesting!

Pedro Tamaroff

03:46

@AlexanderGruber That must have been fun, eh!

Mariano will dictate a course on the representation theory of algebras next semester. I hope I can handle it.

Alexander Gruber

Ohh, I didn't realize he was at your university.

Pedro Tamaroff

(!)

4 hours later…

Tobias Kildetoft

08:15

Cool, I hadn't noticed there was a room like this before.

And it seems like it at least has a bit of activity (not like my failed attempt at a representation theory room on MO)

(ohh, and if we are linking papers, I just updated my paper arxiv.org/abs/1311.1383 in preparation of sending it for publication). Now to get started on converting my dissertation to some papers (there are some finite groups there too)

1 hour later…