Questions tagged [character-theory]
The character-theory tag has no usage guidance.
10
questions with no upvoted or accepted answers
6
votes
0
answers
114
views
Schur indices for 2-groups
I am looking for any results on Schur indices over $\mathbb{Q}$ for 2-groups. By a theorem of Roquette (corollary 10.14 in Isaacs) these numbers are at most 2. I am interested in 2-groups for which ...
5
votes
0
answers
180
views
Information about permutation character from local action
Let $G$ be a finite permutation group acting transitively, but not regularly, on a set $V$. Let $H$ be the stabilizer of some point $v\in V$, and suppose that $H$ acts 2-transitively on one of its (...
4
votes
0
answers
147
views
New characters from old
(All groups in the following discussion are assumed to be finite.)
Character induction is an operation that produces a character of a group given a character of a subgroup. I'm aware that there are ...
3
votes
0
answers
52
views
Index of subgroup generated by characters induced from $p$-elementary subgroups in the ring of virtual characters
I posted this over on MSE, but received absolutely no love. So maybe I’ll have better luck here. It seems like a relatively easy group theory question that I’m just not seeing! It’s on the essential ...
2
votes
0
answers
67
views
Properties of extendable irreducible characters to a normal Sylow subgroup
Let $G$ be a finite group with a nilpotent commutator subgroup, and denote by $mcd(G)$ the set of degrees of the irreducible monomial characters. Suppose $|mcd(g)|=2$. Furthermore, we call a monomial ...
2
votes
0
answers
167
views
The largest number of irreducible characters of the same degree in a finite group
Dear all,
For a finite group $G$, let $m(G)$ denote the largest number of irreducible characters of the same degree of $G$. You can say that $m(G)$ is the largest multiplicity of character degrees of ...
1
vote
0
answers
66
views
How to know the character table of the twisted group algebra of the symmetric group $S_4$
Given the character table of its Schur cover group, is there a way to obtain the character table of twisted group algebra from that? I am particularly interested in the symmetric group $S_4$.
1
vote
0
answers
59
views
Irreducible characters of a semi-direct product with a p-group
Suppose G is a semi-direct product of P with H where P is a (non-abelian) p-group and G is solvable. I wonder what can be said about the irreducible characters of G given information about the ...
1
vote
0
answers
111
views
We know $A_5$ as a non-CI-group. Now, is $A_5$ a BI-group?
We call a group satisfying the following property for all $\nu \in cd(G)$ (Irreducible character degrees of $G$) a BI-group (Babai Invariant group)
Let $G$ be a finite group, let $\Gamma=Cay(G,S)...
1
vote
0
answers
152
views
Do you know any clear classification of groups in which there would exist a unique non-linear character of a given degree?
According to
Lev Kazarin, On Thompson’s Theorem, Journal of Algebra 220, 574–590 (1999)
we know that:
[Corollary 5.3]:Let $$cd(G)=\{\chi(1)|\chi\in Irr(G)\}=\{1,f_1,\dots,f_n,d\}, \;\;n\gt0,$$
...