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Finite groups with odd Sylow automizers

  • Chaida Xu
  • Yuanyang ZhouEmail author
Article
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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 a group.

Keywords

Finite groups Composition factors Irreducible ordinary characters 

Mathematics Subject Classification

20C 
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Notes

Acknowledgements

When preparing the paper, the second author is supported by NSFC (Nos. 11471131 and 11625104). The authors thank the referees for their carefully reading the paper and their helpful comments to improve the paper.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral China Normal UniversityWuhanChina

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