On Supersolubility of a Group with Seminormal Subgroups

Монахов, В. С.; Trofimuk, A. A.

doi:10.1134/s0037446620010103

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2020

2021

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Cited by 4 publications

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“…The factorizable groups G = AB with w-supersoluble factors A and B were investigated in [8], [10], [11], [14]. There are many other papers devoted to study factorizable groups, and the reader is referred to the book [1] and the bibliography therein.…”

Section: Introductionmentioning

confidence: 99%

On the residual of a factorized group with widely supersoluble factors

Монахов¹,

Trofimuk²

2020

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Let P be the set of all primes. A subgroup H of a group G is called P-subnormal in G, if either H = G, or there exists a chain of subgroupsA group G = AB with P-subnormal w-supersoluble subgroups A and B is studied. The structure of its w-supersoluble residual is obtained. In particular, it coincides with the nilpotent residual of the A-residual of G. Here A is the formation of all groups with abelian Sylow subgroups. Besides, we obtain new sufficient conditions for the w-supersolubility of such group G.

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