YOU Ze,LI Bao-jun.Some Sufficient Conditions for Supersolvability ofa Finite Group[J].Journal of Chengdu University of Information Technology,2018,(01):99-102.[doi:10.16836/j.cnki.jcuit.2018.01.017]
有限群超可解的一些充分条件
- Title:
- Some Sufficient Conditions for Supersolvability ofa Finite Group
- 文章编号:
- 2096-1618(2018)01-0099-04
- Keywords:
- fundamental mathematics; algebra; finite group; p-supersoluble; X-s-semipermutable; primary subgroupsCLC number:O152.1
- 分类号:
- O152.1
- 文献标志码:
- A
- 摘要:
- G是有限群且X是一个非空集合。若子群H在G中有补充T,且对任取X中的元x,H与T的任意Sylow子群是X-置换的,子群H被称为是在G中X-s-半置换的.令d 是一个小于P的阶的p-子群的阶.推广了S-半置换子群的一些结果,利用X-s-半置换子群的性质进一步研究有限群,给出有限群超可解的一些结论.即可得到:对任意的d阶正规子群H 和G的可解正规子群X,若H∩Op(G)在G中X-s-半置换的,则G是p-超可解的或者是|P∩Op(G)|>d.
- Abstract:
- Let X be a non-empty subset of G.A subgroup H of a finite group G is said to be X-s-semipermutable in G if H has a supplement T in G such that H is X-permutable with any Sylow subgroup of T for some x∈X.Let P be a sylow p-subgroup of a finite group G,and d a powerof p such that 1≤d<|P|.We derive some theorems and corollaries that extend known results concerning S-semipermutable subgroups.We obtained in this paper that if H∩Op(G)is X-s-semipermutable in G for all normal subgroups H of G with |H|=d,where X is a soluble normal subgroup of G,then either G is p-supersoluble or else |P∩Op(G)|>d.
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备注/Memo
Received date:2017-06-30Foundation item:Project Supported by the National Natural Science Foundation of China(11471055,11371335)