TY - JOUR

T1 - Alternating sums over π-subgroups

AU - Navarro, Gabriel

AU - Sambale, Benjamin

N1 - Funding Information: We thank the anonymous referee for drawing our attention to a theorem of Quillen. The research of the first author is supported by Ministerio de Ciencia e Innovación PID2019-103854GB-I00 . The second author thanks the German Research Foundation (projects SA 2864/1-2 and SA 2864/3-1 ).

PY - 2023/3

Y1 - 2023/3

N2 - 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 π and prove a π-version of Dade's conjecture for π-separable groups. This extends the (known) p-solvable case of the original conjecture and relates to a π-version of Alperin's weight conjecture previously established by the authors.

AB - 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 π and prove a π-version of Dade's conjecture for π-separable groups. This extends the (known) p-solvable case of the original conjecture and relates to a π-version of Alperin's weight conjecture previously established by the authors.

KW - Alternating sums

KW - Dade's conjecture

KW - π-subgroups

UR - http://www.scopus.com/inward/record.url?scp=85137642180&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2022.107227

DO - 10.1016/j.jpaa.2022.107227

M3 - Article

AN - SCOPUS:85137642180

VL - 227

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

M1 - 107227

ER -