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Questions about the branch of algebra that deals with groups.

5 votes
1 answer
177 views

on the group generated by transitive permutation groups and diagonal groups

Let $T$ be a transitive permutation group in $S_n$, embedded in $GL_n(F)$ as permutation matrices. Let $D$ be the group of diagonal matrices in $GL_n(F)$. Let $G$ be the group generated by $T$ and $D$ …
Jimmy's user avatar
  • 565
4 votes
1 answer
361 views

the number of indecomposable modules of finite groups over finite fields of a fixed dimension

I am interested in determining the the number of indecomposable modules of finite groups over finite fields of a fixed dimension. Specifically, I have the following conjecture: Conjecture. Suppose we …
Jimmy's user avatar
  • 565
6 votes
2 answers
641 views

to test equivalence of representations under automorphism

Hi all, I would like to propose the following problem: Given two representations $\rho$ and $\tau$ of a group $G$ over complex number, we would like to know if there exists an automorphism $\phi$, s …
Jimmy's user avatar
  • 565
3 votes
0 answers
257 views

The fraction of groups with normal Hall subgroups

Dear all, I am a student on computer science. So please forgive me if I state some results in a weird way, and I hope I ask an interesting question to you. The question is related to finite groups w …
Jimmy's user avatar
  • 565
3 votes

Given a normal subgroup N⊆G, when does G contain a subgroup isomorphic to G/N?

A good theorem related to your problem is Schur-Zassenhaus theorem. It states that when the normal subgroup N is a Hall subgroup, namely the order of N and the index of N are coprime, then there exist …
Jimmy's user avatar
  • 565