Permutability of the Sylow 2-subgroup with some biprimary subgroups
https://doi.org/10.29235/1561-2430-2018-54-4-460-467
Abstract
In this paper, the compositional structure of a finite group G is investigated, which has the Sylow 2-subgroup that is permutable with some non p-nilpotent biprimary subgroups, which contain the Sylow р-subgroup of G for all odd simple divisors of the р order of the group G, and such biprimary subgroups are taken one by one for each odd р, and mark the set SB(G). In this work, the existence of the subset SB(G)* in SB(G) is proved, which consists of р-closed subgroups. The main result of this paper is as follows: if the Sylow 2-subgroup of the group G is permutable with all subgroups SB(G)*, then G may have simple non-abelian compositional factors only of L2 (7) type, if p > 3, and additionally of L2 (3f) type, f = 3a , a ≥ 1, if p = 3.
About the Author
S. Y. Bashun
Polotsk State University
Belarus
Senior Lecturer of Higher Mathematics Department
Belarus
Senior Lecturer of Higher Mathematics Department
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