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A NOTE ON NORMAL COMPLEMENTS FOR FINITE GROUPS

Published online by Cambridge University Press:  29 April 2018

NING SU
Affiliation:
Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China email suning3@mail.sysu.edu.cn
ADOLFO BALLESTER-BOLINCHES*
Affiliation:
Departament de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain email Adolfo.Ballester@uv.es
HANGYANG MENG
Affiliation:
Departament de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain email hangyangmenges@gmail.com
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Abstract

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Assume that $G$ is a finite group and $H$ is a 2-nilpotent Sylow tower Hall subgroup of $G$ such that if $x$ and $y$ are $G$-conjugate elements of $H\cap G^{\prime }$ of prime order or order 4, then $x$ and $y$ are $H$-conjugate. We prove that there exists a normal subgroup $N$ of $G$ such that $G=HN$ and $H\cap N=1$.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author is supported by the National Natural Science Foundation of China (no. 11401597). The second and third authors have been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economía y Competitividad, Spain, and FEDER, European Union. The second author is also supported by Prometeo/2017/057 of Generalitat (Valencian Community, Spain) and the third author is also supported by the China Scholarship Council, grant no. 201606890006.

References

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