Skip to main content

All Questions

9 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
24 votes
0 answers
813 views

Revising the proof of CFSG

This is an oft-quoted excerpt from John Thompson's article "Finite Non-Solvable Groups": “... the classification of finite simple groups is an exercise in taxonomy. This is obvious to the ...
semisimpleton's user avatar
12 votes
0 answers
340 views

Does every finite group have a small projective representation (over some ring)?

Question. Let $G$ be a finite group. Can we find some (commutative) ring $R$ and some positive integer $d=O(\log\lvert G\rvert)$ such that $G$ can be found as a subgroup of $\operatorname{PGL}_d(R)$? ...
Carl Schildkraut's user avatar
12 votes
0 answers
420 views

Non-isomorphic groups with same character tables and different Brauer character tables

Let $A$ be a discrete valuation ring with perfect residue field $k$ of characteristic $p$ and field of fractions $K$ of characteristic $0$. Let $G$ and $H$ be two finite groups and assume that $K$ is ...
Sebastian A. Spindler's user avatar
3 votes
0 answers
109 views

Exact structures on representations of a finite group

For simplicity assume $G$ is a (finite) $p$-group, and $k$ is field of characteristic $p$, so that there exists a unique simple $kG$-module the trivial module $k$. I am looking for a class of short ...
Justin Bloom's user avatar
3 votes
0 answers
133 views

Isomorphism of certain irreducible representations over finite fields

We are given a faithful representation of a cyclic group of order 5 $\rho: C_5=G \rightarrow End_{\mathbb{F}_3}(V) $ with $dim_{\mathbb{F}_3}V=8$ as vector space. It is also known that $V=U\oplus W$ ...
Gregory Eritsyan's user avatar
2 votes
0 answers
57 views

Brauer pairs associated to a normalizer subsystem in the fusion system of a block of a finite group

Let $G$ be a finite group and let $k$ be an algebraically closed field of positive characteristic $p$. Let $b$ be a block of $kG$ and let $(P,e)$ be a maximal $(G,b)$-Brauer pair. For every subgroup $...
John McHugh's user avatar
2 votes
0 answers
116 views

Loewy structure of $S_4$

How to deduce the Loewy Structure of $kS_4$ where $k$ has characteristic 2. I can compute the Cartan matrix and Decomposition matrix with Brauer Characters without difficulties. But when it comes to ...
user666's user avatar
  • 51
1 vote
0 answers
129 views

$G$-invariant bilinear maps

Let $G$ be a finite group and $M$ a finitely generated $\mathbb{Z}G$-module. Then $M \otimes k$ is a representation of $G$ for any field $k$. I am interested in the number of ways we can turn $M \...
Michiel Van Couwenberghe's user avatar
1 vote
0 answers
54 views

Largest almost quasisimple group that acts on a spin module

I'd like to know the largest almost quasisimple group $G$ which acts faithfully and irreducibly on the spin module for an odd dimensional orthogonal group $\Omega(2k+1,q)$, or on each of the two half-...
ChockaBlock's user avatar