Search 205,682,721 papers from all fields of science

Search

Sign InCreate Free Account

Corpus ID: 240353912

Codegrees of primitive characters of solvable groups

@inproceedings{Jin2021CodegreesOP,
title={Codegrees of primitive characters of solvable groups},
author={Ping Jin and Lei Wang and Yong Yang},
year={2021}
}

We obtain the codegree of a certain primitive character for a finite solvable group, and thereby give a negative answer to a question proposed by Moretó in [8].

Abstract Let G be a finite group, let
${\mathrm{Irr}}(G)$
be the set of all irreducible complex characters of G and let
$\chi \in {\mathrm{Irr}}(G)$
. Define the codegrees,
${\mathrm{cod}}(\chi… Expand

The result of this note is as follows. If a finite solvable group has an element of order m, then the group has an irreducible character whose codegree contains all prime divisors of m.

Let $${g \in G}$$ , where G is an arbitrary finite group. Then there exists $${\chi \in {\rm Irr} (G)}$$ such that $${{\rm ker}(\chi) \cap \langle g \rangle = 1}$$ and every prime divisor of the… Expand

Introduction. In the theory of group characters, modular representation theory has explained some of the regularities in the behavior of the irreducible characters of a finite group; not… Expand