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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2010, Issue 1(2), Pages 28–30
(Mi pfmt154)
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MATHEMATICS
On UΦ-hypercentre of finite groups
V. A. Kovaleva, A. N. Skiba F. Skorina Gomel State University, Gomel
Abstract:
The product of all normal subgroups of G whose all non-Frattini G-chief factors are cyclic is called the UΦ-hypercentre of G. The following theorem is proved. Theorem. Let X⩽E be soluble normal subgroups of G. Suppose that every maximal subgroup of every Sylow subgroup of X conditionally covers or avoids each maximal pair (M,G), where MX=G. If X is either E or F(E), then. E⩽ZUΦ(G).
Keywords:
UΦ-hypercentre, supersoluble group, maximal pair, (conditionally) cover-avoidance property of subgroups, CAP-subgroup.
Received: 27.01.2010
Citation:
V. A. Kovaleva, A. N. Skiba, “On UΦ-hypercentre of finite groups”, PFMT, 2010, no. 1(2), 28–30
Linking options:
https://www.mathnet.ru/eng/pfmt154 https://www.mathnet.ru/eng/pfmt/y2010/i1/p28
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Abstract page: | 166 | Full-text PDF : | 75 | References: | 41 |
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