On p-nilpotency of finite groups with some subgroups π-quasinormally embedded

Yangming Li; Yanming Wang; Huaquan Wei

doi:10.1007/s10474-005-0225-8

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Acta Mathematica Hungarica

Volume/Issue:: Volume 108: Issue 4

On p-nilpotency of finite groups with some subgroups π-quasinormally embedded

Authors:

Yangming Li

Yangming Li Department of Mathematics, Guangdong Institute of Education Guangzhou, 510310, P.R. China

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Yanming Wang

Yanming Wang Department of Mathematics, Zhongshan University Guangzhou, 510275, P.R. China

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Huaquan Wei

Huaquan Wei Department of Mathematics, Guangxi Teacher’s College Nanning, 530001, P.R. China

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Pages:: 283–298

Online Publication Date:: 08 Sep 2005

Publication Date:: 01 Aug 2005

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10474-005-0225-8

Keywords:: p-nilpotent group; maximal subgroup; 2-maximal subgroup; minimal subgroup; subgroup of prime square order; ?-quasinormally embedded subgroup

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Summary A subgroup H of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, and H is said to be π-quasinormally embedded in G if for each prime dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroups of G. We characterize p-nilpotentcy of finite groups with the assumption that some maximal subgroups, 2-maximal subgroups, minimal subgroups and 2-minimal subgroups are π-quasinormally embedded, respectively.

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Acta Mathematica Hungarica

Print ISSN:: 0236-5294

Online ISSN:: 1588-2632

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Acta Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1950
Volumes per Year	3
Issues per Year	6
Founder	Magyar Tudományos Akadémia
Founder's Address	H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0236-5294 (Print)
ISSN	1588-2632 (Online)