On the permutability of Sylow subgroups with derived subgroups of B-subgroups
A finite non-nilpotent group G is called a B-group if every proper subgroup of the quotient group G/Φ(G) is nilpotent. We establish the r-solvability of the group in which some Sylow r-subgroup permutes with the derived subgroups of 2-nilpotent (or 2-closed) B-subgroups of even order and the solvab...
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Format: | Article |
Language: | Belarusian |
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Belarusian State University
2019-04-01
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Series: | Журнал Белорусского государственного университета: Математика, информатика |
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Online Access: | https://journals.bsu.by/index.php/mathematics/article/view/924 |
Summary: | A finite non-nilpotent group G is called a B-group if every proper subgroup of the quotient group G/Φ(G) is nilpotent. We establish the r-solvability of the group in which some Sylow r-subgroup permutes with the derived subgroups of 2-nilpotent (or 2-closed) B-subgroups of even order and the solvability of the group in which the derived subgroups of 2-closed and 2-nilpotent B-subgroups of even order are permutable. |
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ISSN: | 2520-6508 2617-3956 |