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Research Article | Open Access

Normalizer property of finite groups with almost simple subgroups

Jingjing Hai1( ), Xian Ling2
College of Quality and Standardization, Qingdao University, Qingdao 266071, China
College of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
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Abstract

In this paper, we prove that all Coleman automorphisms of extension of an almost simple group by an abelian group or a simple group are inner. Using our methods we also show that the Coleman automorphisms of 2-power order of an odd order group by an almost simple group are inner. In particular, these groups have the normalizer property.

Keywords

almost simple groupsimple groupColeman automorphismq-central automorphismnormalizer property

References

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Electronic Research Archive
Volume 30 Issue 11,
November 2022
Pages 4232-4237
DOI: 10.3934/era.2022215

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Cite this article:
Hai J, Ling X. Normalizer property of finite groups with almost simple subgroups. Electronic Research Archive, 2022, 30(11): 4232-4237. https://doi.org/10.3934/era.2022215

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Received: 18 June 2022
Revised: 01 September 2022
Accepted: 03 September 2022
Published: 15 November 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)