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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 2, Pages 259–275
DOI: https://doi.org/10.17377/smzh.2016.57.203
(Mi smj2742)
 

This article is cited in 17 scientific papers (total in 17 papers)

Finite groups with generalized subnormal embedding of Sylow subgroups

A. F. Vasil'eva, T. I. Vasil'evab, A. S. Vegeraa

a Francisk Skaryna Gomel State University, Gomel, Belarus
b Belarusian State University of Transport, Gomel, Belarus
References:
Abstract: Given a set $\pi$ of primes and a hereditary saturated formation $\mathfrak F$, we study the properties of the class of groups $G$ for which the identity subgroup and all Sylow $p$-subgroups are $\mathfrak F$-subnormal ($\mathrm K$-$\mathfrak F$-subnormal) in $G$ for each $p$ in $\pi$. We show that such a class is a hereditary saturated formation and find its maximal inner local screen. Some criteria are obtained for the membership of a group in a hereditary saturated formation in terms of its formation subnormal Sylow subgroups.
Keywords: finite group, Sylow subgroup, formation, hereditary saturated formation, $\mathfrak F$-subnormal subgroup, $\mathrm K$-$\mathfrak F$-subnormal subgroup, local screen.
Received: 24.04.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 2, Pages 200–212
DOI: https://doi.org/10.1134/S0037446616020038
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: A. F. Vasil'ev, T. I. Vasil'eva, A. S. Vegera, “Finite groups with generalized subnormal embedding of Sylow subgroups”, Sibirsk. Mat. Zh., 57:2 (2016), 259–275; Siberian Math. J., 57:2 (2016), 200–212
Citation in format AMSBIB
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  • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Сибирский математический журнал Siberian Mathematical Journal
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