Questions tagged [gr.group-theory]
Questions about the branch of algebra that deals with groups.
8,474 questions
3
votes
0
answers
150
views
How does $\text{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p)$ act on $\text{Irr}(G)$?
Let $G$ be a finite group. For a field $F$ (algebraically closed of characteristic $0$), let $\text{Irr}_F(G)$ denote the irreducible characters of $G$ over $F$.
$\text{Gal}(\mathbb{C/R})$ acts on $\...
- 2,121
3
votes
0
answers
107
views
On number of subgroups of finite non-abelian simple groups
It is known that there exist non-isomorphic non-abelian finite simple groups with same order. For example one can refer to: Non-isomorphic finite simple groups
My question is: Can there be two non-...
- 341
5
votes
1
answer
97
views
How can one obtain an inclusion of an induced module and the cokernel thereof with MAGMA?
I would like to ask a MAGMA question.
In the MAGMA code below,
...
- 319
3
votes
0
answers
77
views
Subgroup structure of $\mathrm{J}_4$
Up to isomorphism, there are two groups which are maximal subgroups of both of the simple groups $\mathrm{M}_{24}$ and $\mathrm{L}_5(2)$ (using ATLAS notation). These have structure $2^4:\mathrm{A}_8$ ...
- 3,183
4
votes
0
answers
153
views
Simplicial structure of outer space
Let $CV_n^r$ denote Culler-Vogtmann reduced outer space (graphs do not have separating edges) (see Moduli of graphs and automorphisms of free groups for reference), and let $G$ be a marked graph in ...
- 439
6
votes
0
answers
78
views
A query regarding maximal subgroups of a finite non-solvable group
This is some kind of continuation of an earlier MO post: Existence of maximal subgroups of even order which are not normal
It appeared in a comment in the above post. I believe the following is true:
...
- 341
0
votes
0
answers
54
views
Functional of PSD functions over finite group
Let $G$ be a finite (possibly non-abelian) group and let $f:G\to\mathbb{R}$ be an even function, i.e. $f(g)=f(g^{-1})$ for all $g\in G$. Moreover, let $f$ satisfies $\sum_G f(g)\geq 0$. Call $f$ ...
- 441
4
votes
1
answer
222
views
RT-structures in finite groups
During my research in Algebraic Geometry, I was led to the following problem in Combinatorial Group Theory, strictly related to finite quotients of pure surface braid groups.
Let $G$ be a finite group....
- 68.2k
1
vote
0
answers
280
views
Linear operations over finite (non-abelian) group
Let $G$ be a finite group (non-abelian), $S_1,S_2\subseteq G$, $S_1\cap S_2=\emptyset $ and $|S_1|=|S_2|.$
Let $L$ be a $k\times m$ matrix such that every row has exactly one 1 and one -1, other ...
- 441
5
votes
1
answer
286
views
Is every 2-divisible group without elements of order 2 uniquely 2-divisible?
Definition. A group $G$ is called (uniquely) $2$-divisible if for every $g\in G$ there exists a (unique) element $x\in G$ such that $x^2=g$.
It is clear that an abelian group is uniquely 2-divisible ...
- 44k
7
votes
2
answers
415
views
Topological full groups
I am trying to learn about topological full groups to do a masters dissertation on this, and am trying to find a solid path to do so. I do not have any C* algebra or dynamics background. What would be ...
- 71
1
vote
1
answer
109
views
Composition factors of induced representations of semi-direct products
As I have not yet recieved any answers, this question is cross-posted from stack exchange
Let $H$ be a subgroup of a finite group $G$ and let $\phi:\mathbb{Z}/2\to \text{Aut}(G)$ such that $\phi(1)(H)=...
9
votes
1
answer
972
views
What is this theorem in Egorov 1981?
In a paper by Wise it is claimed that:
[...] Egorov proved the residual finiteness of positive one-relator groups where the relator is of the form $W^n$ and $n\geq 2$.
A paper by Baumslag, Miller, ...
- 491
5
votes
2
answers
548
views
Infinite hyperbolic group contains infinite order elements
I'm currently working on hyperbolic groups and keep coming across the statement that the number of conjugacy classes of torsion elements is finite. I've also proven this statement using a Dehn ...
- 51
3
votes
0
answers
151
views
Combinatorial criterion for conjugacy of Coxeter elements in a right-angled Artin group
Let $G=(V,E)$ be a simple (finite) graph, and form the associated right-angled Artin group $W =\langle x_v, v \in V \mid x_ux_v = x_vx_u\textrm{ for $\{u,v\}\notin E$}\rangle$. (Note that the edges ...
- 25.8k