Solution of Brauer's k(B)-Conjecture for pi-blocks of pi-separable groups
Representation Theory
2017-11-10 v2
Abstract
Answering a question of P\'alfy 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.
Keywords
Cite
@article{arxiv.1706.09572,
title = {Solution of Brauer's k(B)-Conjecture for pi-blocks of pi-separable groups},
author = {Benjamin Sambale},
journal= {arXiv preprint arXiv:1706.09572},
year = {2017}
}
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