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Algebra i logika, 2016, Volume 55, Number 5, Pages 531–539
DOI: https://doi.org/10.17377/alglog.2016.55.501 (Mi al759) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Abnormality criteria for $p$-complements

E. P. Vdovinab, D. O. Revinab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
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DOI: https://doi.org/10.17377/alglog.2016.55.501
Abstract: It is proved that for any finite group $G$ possessing a $p$-complement $H$ for some prime number $p$, the following assertions are equivalent: (1) all $p$-complements of $G$ are selfnormalizable; (2) all $p$-complements of $G$ are abnormal; (3) the subgroup $H$ is abnormal in $G$; (4) $NG(HX)=HX$ for any $X\trianglelefteq G$; (5) $G$ does not contain central chief pfactors.
Keywords: $p$-complement, abnormal subgroup, pronormal subgroup, Hall subgroup.
Funding agency Grant number
Novosibirsk State University
Supported by International Mathematical Center of Novosibirsk State University.
Received: 20.06.2016
English version:
Algebra and Logic, 2016, Volume 55, Issue 5, Pages 347–353
DOI: https://doi.org/10.1007/s10469-016-9406-5
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: E. P. Vdovin, D. O. Revin, “Abnormality criteria for $p$-complements”, Algebra Logika, 55:5 (2016), 531–539; Algebra and Logic, 55:5 (2016), 347–353
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    		Алгебра и логика Algebra and Logic
     
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