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arXiv · 1706.09572

Solution of Brauer's k(B)-Conjecture for pi-blocks of pi-separable groups

Benjamin Sambale
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Abstract

Answering a question of Pálfy and Pyber, we first prove the following extension of the k(GV)-Problem: Let G be a finite group and A\le Aut(G) such that (|G|,|A|)=1. Then the number of conjugacy classes of the semidirect product GA is at most |G|. As a consequence we verify Brauer's k(B)-Conjecture for pi-blocks of pi-separable groups which was proposed by Y. Liu. We also discuss equality in Brauer's Conjecture. On the other hand, we construct a counterexample to a version of Olsson's Conjecture for pi-blocks which was also introduced by Liu.

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Benjamin Sambale. 2017-11-09. Solution of Brauer's k(B)-Conjecture for pi-blocks of pi-separable groups. https://arxiv.org/abs/1706.09572

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