Alternating sums over pi-subgroups

authored by

Gabriel Navarro, Benjamin Sambale

Abstract

Dade's conjecture predicts that if p is a prime, then the number of irreducible characters of a finite group of a given p-defect is determined by local subgroups. In this paper we replace \(p\) by a set of primes pi and prove a pi-version of Dade's conjecture for pi-separable groups. This extends the (known) p-solvable case of the original conjecture and relates to a pi-version of Alperin's weight conjecture previously established by the authors.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Preprint

Publication date

23.09.2021

Publication status

E-pub ahead of print

Electronic version(s)

http://arxiv.org/abs/2109.11198v1 (Access: Open)