Finite groups with odd Sylow automizers

Chaida Xu; Yuanyang Zhou

Finite groups with odd Sylow automizers

Group Theory 2018-07-27 v2 Representation Theory

Authors: Chaida Xu , Yuanyang Zhou

Abstract

Let $p$ be an odd prime number. In this paper, we characterize the nonabelian composition factors of a finite group with odd $p$ -Sylow automizers, and then prove that the McKay conjecture, the Alperin weight conjecture and the Alperin-McKay conjecture hold for such group.

Keywords

finite groups finite group theory group theory

Cite

@article{arxiv.1807.00552,
  title  = {Finite groups with odd Sylow automizers},
  author = {Chaida Xu and Yuanyang Zhou},
  journal= {arXiv preprint arXiv:1807.00552},
  year   = {2018}
}

Comments

In this new version, we modify some errors in the first version: we add Lemma 2.1 and rewrite the proof for the case $S=D_4(q)$ and $p=3$ in the proof of Lemma 3.7

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