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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2018, Issue 4(37), Pages 103–105
(Mi pfmt612)
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MATHEMATICS
On the generalized norm of a finite group
V. M. Selkina, N. S. Kosenokb a F. Scorina Gomel State University
b Belarusian Trade and Economic University of Consumer Cooperatives
Abstract:
Let G be a finite group and π={p1,…,pn}⊆P. Then G is called π-special if G=Op1(G)×⋯×Opn(G)×Oπ′(G). We use Nπsp to denote the class of all finite π-special groups. Let Nπsp be the intersection of the normalizers of the π-special residuals of all subgroups of G, that is, Nπsp(G)=⋂H⩽GNG(HNπsp). We say that Nπsp is the π-special norm of G. We study the basic properties of the π-special norm of G. In particular, we prove that Nπsp is π-soluble.
Keywords:
finite group, π-special group, π-soluble group, π-special residual of a group, π-special norm of a group.
Received: 13.11.2018
Citation:
V. M. Selkin, N. S. Kosenok, “On the generalized norm of a finite group”, PFMT, 2018, no. 4(37), 103–105
Linking options:
https://www.mathnet.ru/eng/pfmt612 https://www.mathnet.ru/eng/pfmt/y2018/i4/p103
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Abstract page: | 128 | Full-text PDF : | 39 | References: | 24 |
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