On the permutability of Sylow subgroups with derived subgroups of B-subgroups

  • Ekaterina V. Zubei Francisk Skorina Gomel State University, 104 Saveckaja Street, Gomel 246007, Belarus
DOI: https://doi.org/10.33581/2520-6508-2019-1-12-17

Abstract

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.

Author Biography

Ekaterina V. Zubei, Francisk Skorina Gomel State University, 104 Saveckaja Street, Gomel 246007, Belarus

postgraduate student at the department of algebra and geometry, faculty of mathematics and programming technologies

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Published
2019-04-08
Keywords: finite group, r-solvable group, Sylow subgroup, B-group, the derived subgroup, permutable subgroups
How to Cite
Zubei, E. V. (2019). On the permutability of Sylow subgroups with derived subgroups of B-subgroups. Journal of the Belarusian State University. Mathematics and Informatics, 1, 12-17. https://doi.org/10.33581/2520-6508-2019-1-12-17
Issue
No 1 (2019): Journal of the Belarusian State University. Mathematics and Informatics
Section
Mathematical Logic, Algebra and Number Theory

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