On Huppert’s ρ - σ conjecture for blocks

authored by

Christine Bessenrodt, Yang Liu, Ziqun Lu, Jiping Zhang

Abstract

For n∈ N, we denote by π(n) the set of prime divisors of n. For a block B of a finite group G, let Irr(B) be the set of irreducible complex characters of G belonging to B. Let ρ(B) be the set of those primes dividing the degree of some character in Irr(B), and let σ(B) be the maximal number of primes dividing such a degree. For a solvable group G, we prove that | ρ(B) | ≤ 3 σ(B) + 1. This provides a block result in the spirit of Huppert’s ρ-σ conjecture.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Tianjin Normal University
Tsinghua University
Peking University

Type

Article

Journal

Archiv der Mathematik

Volume

118

Pages

339-347

No. of pages

9

ISSN

0003-889X

Publication date

04.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

https://doi.org/10.1007/s00013-021-01696-9 (Access: Closed)