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On weakly s-permutably embedded subgroups of finite groups (II)
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作者 Yujian HUANG Yangming LI Shouhong QIAO 《Frontiers of Mathematics in China》 SCIE CSCD 2013年第4期855-867,共13页
Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably embedded in G if for each prime p dividing |H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgrou... Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably embedded in G if for each prime p dividing |H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgroup of G; H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G = HT and H n T ≤ Hse. In this paper, we continue the work of [Comm. Algebra, 2009, 37: 1086-1097] to study the influence of the weakly s-permutably embedded subgroups on the structure of finite groups, and we extend some recent results. 展开更多
关键词 s-Permutable subgroup s-permutably embedded subgroup weakly s-permutably embedded subgroup p-nilpotent group
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Some open questions in the theory of generalized permutable subgroups 被引量:11
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作者 GUO WenBin XIE FengYan LI BaoJun 《Science China Mathematics》 SCIE 2009年第10期2132-2144,共13页
A subgroup H of a group G is said to be weakly s-supplemented in G if H has a supplement T in G such that H ∩ T HsG, where HsG is the largest s-permutable subgroup of G contained in H. This paper constructs an exampl... A subgroup H of a group G is said to be weakly s-supplemented in G if H has a supplement T in G such that H ∩ T HsG, where HsG is the largest s-permutable subgroup of G contained in H. This paper constructs an example to show that the open questions 6.3 and 6.4 in J Algebra, 315: 192–209 (2007) have negative solutions, and shows that in many cases Question 6.4 is positive. A series of known results are unified and generalized. 展开更多
关键词 finite group formations weakly s-supplemented subgroup maximal subgroup minimal subgroup 20D10 20D20
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