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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
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
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
Linking options:
https://www.mathnet.ru/eng/smj2742 https://www.mathnet.ru/eng/smj/v57/i2/p259
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Abstract page: | 380 | Full-text PDF : | 95 | References: | 60 | First page: | 7 |
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