A note on Hall S-permutably embedded subgroups of finite groups
Vernadsky National Library of Ukraine
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| Title |
A note on Hall S-permutably embedded subgroups of finite groups
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| Creator |
Sinitsa, D.
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| Description |
Let G be a finite group. Recall that a subgroup A 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.
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| Date |
2019-06-17T18:59:06Z
2019-06-17T18:59:06Z 2017 |
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| Type |
Article
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| Identifier |
A note on Hall S-permutably embedded subgroups of finite groups / D. Sinitsa // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 305-311. — Бібліогр.: 9 назв. — англ.
1726-3255 2010 MSC:20D10, 20D15, 20D30. http://dspace.nbuv.gov.ua/handle/123456789/156024 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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