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The influence of X-semipermutability of subgroups on the structure of finite groups |
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| Authors: | CHEN GuiYun & LI JinBao School of Mathematics Statistics Southwest University Chongqing China School of Mathematical Sciences Xuzhou Normal University Xuzhou China |
| Affiliation: | CHEN GuiYun1 & LI JinBao2 1 School of Mathematics , Statistics,Southwest University,Chongqing 400715,China 2 School of Mathematical Sciences,Xuzhou Normal University,Xuzhou 221116,China |
| Abstract: | Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained. |
| Keywords: | finite groups X-semipermutable subgroups supersoluble groups p-nilpotent groups subnormal subgroups Sylow subgroups cyclic subgroups |
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