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Research Article | Open Access

The normalizer problem for finite groups having normal 2-complements

Jidong Guo, Liang Zhang, Jinke Hai( )
College of Mathematics and Statistics, Yili Normal University, Yining 835000, China
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Abstract

Assume that H is a finite group that has a normal 2-complement. Under some conditions, it is proven that the normalizer property holds for H. In particular, if there is a nilpotent subgroup of index 2 in H, then H has the normalizer property. The result of Li, Sehgal and Parmenter, stating that the normalizer property holds for finite groups that have an abelian subgroup of index 2 is generalized.

Keywords

the normalizer propertyColeman automorphismsclass-preserving automorphismsnormal 2-complements

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Electronic Research Archive
Volume 32 Issue 8,
August 2024
Pages 4905-4912
DOI: 10.3934/era.2024225

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Cite this article:
Guo J, Zhang L, Hai J. The normalizer problem for finite groups having normal 2-complements. Electronic Research Archive, 2024, 32(8): 4905-4912. https://doi.org/10.3934/era.2024225

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Received: 07 May 2024
Revised: 02 August 2024
Accepted: 08 August 2024
Published: 15 August 2024
©2024 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)