All Questions
7 questions
9
votes
1
answer
508
views
When is the augmentation ideal projective as RG-module?
Let $G$ be a finite group and let $R$ be a commutative ring.
I'd like to ask, if there is a theorem of the following kind:
The augmentation ideal $I_G$ is projective as RG-module, if and only if ... ?...
- 1,755
4
votes
1
answer
273
views
Wedderburn decomposition of special linear groups
$\DeclareMathOperator\SL{SL}\newcommand\card[1]{\lvert#1\rvert}$I want to study about Wedderburn decomposition of group algebra $k\SL(n,\mathbb{F}_p)$ where $k$ is either an algebraically closed field ...
- 249
4
votes
1
answer
686
views
Character theory of $2$-Frobenius groups.
This is a crosspost of my (slightly longer) question on MSE since I'm not getting any responses there.
Definition. Let $G$ be a finite group and $F_1=\text{Fit}\,G$ and $F_2/F=\text{Fit}\left(G/...
- 1,173
4
votes
0
answers
218
views
Conjugacy class representatives for the automorphism group of a finite abelian group
Given a finite abelian group $A$, I'd like a list of conjugacy class representatives for its automorphism group ${\rm Aut}(A)$.
In fact, it's not important that I have exactly one representative from ...
- 286
2
votes
0
answers
91
views
Reference request: structure of group of units of finite group ring
Let $G$ be a finite group, let $F$ be a finite field and let $F[G]$ be the group algebra of $G$ over $F$.
What is known about the structure of the group of units $F[G]^\times$? Of course, it must ...
- 1,433
1
vote
0
answers
123
views
Four octonionic loops to identify
A loop is a quasigroup with the identity. I have to disclose that loop-theory is something outside my expertise.
I have four loops arising from octonionic elements of unitary norm that have order 16, ...
- 295
1
vote
0
answers
136
views
Representations of finite groups over commutative rings-question and reference request
In a textbook of representation theory I have encountered the following statement without proof:
Let $R$ be a commutative ring and $G$ a finite group. If $M$ is a simple $RG$-module then the ...
- 137