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Alternating sums over π-subgroups

Institution:	1. Department of Mathematics, Universitat de València, 46100 Burjassot, València, Spain;2. Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany;1. Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 Japan;2. Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 Japan;1. CIEM-FaMAF, CONICET-Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina;2. Guangdong Technion Israel Institute of Technology, 241 Daxue Road, Jinping District, Shantou, Guandong Province, China;1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Napoli, Italy;2. School of Mathematical Sciences, Queen Mary University of London, London, England, United Kingdom

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 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.

Keywords:	Dade's conjecture Alternating sums
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