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6
votes
2answers
267 views

Subgroups from which all class functions extend to class functions on the ambient group

Until someone suggests better terminology, let me call a subgroup H of a finite group G segregated if every class function on H can be extended to a class function on G. Equivalently, H should have ...
0
votes
0answers
108 views

a problem in character theory of finite group

I want to ask a question on character theory of finite group. Let $G$ be a finite nonablian group, and let $p$ be the minimal divisior of |G|=n. Suppose $\chi\in IRR(G)$. Let $A=Gal(Q_n/Q)$. $A$ ...
3
votes
1answer
310 views

Is there any groups $G$ with the property $(*_d)$?

Let $G$ be a finite group of even order has only one non-principal irreducible character $\chi$ of degree $d$, $d\in \mathbb{N}$, with the following property (we name it $(*_d)$): $(*_d)$: There ...
2
votes
0answers
121 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 $$cd(G)=\{\chi(1)|\chi\in Irr(G)\}=\{1,f_1,\dots,f_n,d\}, \;\;n\gt0,$$ ...
6
votes
0answers
167 views

A constant associated to the character table of a finite group

Following on from some of myprevious MO questions on finite group theory... $\newcommand{\Irr}{\operatorname{Irr}}\newcommand{\Conj}{\operatorname{Conj}}\newcommand{\AMZL}{{\rm AM}_{\rm Z}}$ Let $G$ ...
2
votes
2answers
144 views

reference request for character theory of p-extraspecial groups

In a recent preprint 1302.1929 my co-authors and I make use of some results about the character theory of extraspecial groups. These were largely gleaned from haphazard Googling, comments made by ...
2
votes
0answers
127 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 ...
5
votes
0answers
107 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 ...