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# A note on Hall S-permutably embedded subgroups of finite groups

 dc.contributor.author Sinitsa, D.A. dc.date.accessioned 2020-01-15T10:22:23Z dc.date.available 2020-01-15T10:22:23Z dc.date.issued 2017 dc.identifier.uri http://hdl.handle.net/123456789/4675 dc.description Sinitsa D.A. A note on Hall S-permutably embedded subgroups of finite groups / D.A.Sinitsa // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp.305- 311 uk_UA dc.description.abstract Let G be a finite group. Recall that a subgroup A uk_UA of G is said to permute with a subgroup B if AB = BA. A subgroup A of G is said to be S-quasinormal or S-permutable in G if A permutes with all Sylow subgroups of G. Recall also that HsG is the S-permutable closure of H in G, that is, the intersection of all such S-permutable subgroups of G which contain H. We say that H is Hall S-permutably embedded in G if H is a Hall subgroup of the S-permutable closure HsG of H in G. We prove that the following conditions are equivalent: (1) every subgroup of G is Hall S-permutably embedded in G; (2) the nilpotent residual GN of G is a Hall cyclic of square-free order subgroup of G; (3) G = D ⋊ M is a split extension of a cyclic subgroup D of square-free order by a nilpotent group M, where M and D are both Hall subgroups of G. dc.language.iso en uk_UA dc.publisher ДЗ "ЛНУ імені Тараса Шевченка" uk_UA dc.relation.ispartofseries математичні науки; dc.subject S-permutable subgroup uk_UA dc.subject Hall S-permutably embed- ded subgroup uk_UA dc.subject Sylow subgroup uk_UA dc.subject supersoluble group uk_UA dc.subject maximal subgroup uk_UA dc.title A note on Hall S-permutably embedded subgroups of finite groups uk_UA dc.type Article uk_UA
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