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Results tagged with gr.group-theory
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user 8012
Questions about the branch of algebra that deals with groups.
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 …
- 565
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 $D$ …
- 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 …
- 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 …
- 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 …
- 565