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arXiv · 2109.11198

Alternating sums over pi-subgroups

Gabriel Navarro·Benjamin Sambale
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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.

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Gabriel Navarro, Benjamin Sambale. 2021-09-23. Alternating sums over pi-subgroups. https://arxiv.org/abs/2109.11198

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