Alternating sums over pi-subgroups

DOI10.1016/J.JPAA.2022.107227arXiv2109.11198MaRDI QIDQ6378363

Publication date: 23 September 2021

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.

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Modular representations and characters (20C20)

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