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]

@AlexanderGruber This is nice.

@PedroTamaroff I'm liking it my friend!

@AlexanderGruber You should post a weekly problem!

@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.

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?

It is done.

Yay.

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

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.

@AlexanderGruber Alex.

You know what always bugged me?

@PedroTamaroff What's that?

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

I never grokked it.

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

@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.

@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!

@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.

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

(!)

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)

Cool beans @AlexanderGruber

Nice room.

@AlexanderGruber BTW, what sort of things are you working on now?

@TobiasKildetoft He was doing graph theoretic group theory the last time I saw (not coarse geometry).

And nice to see you here.