有限群超可解的一些充分条件（英文）  

Some Sufficient Conditions for Supersolvability of a Finite Group

作　　者：尤泽 李保军 YOU Ze, LI Bao-jun(College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610025, Chin)

机构地区：[1]成都信息工程大学应用数学学院,四川成都610025

出　　处：《成都信息工程大学学报》2018年第1期99-102,共4页Journal of Chengdu University of Information Technology

基　　金：Project Supported by the National Natural Science Foundation of China(11471055,11371335);the Scientific Research Foundation of CUIT(J201512)

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∩O^p(G)在G中X-s-半置换的,则G是p-超可解的或者是|P∩O^p(G)|>d.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 psubgroup 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 ∩ O^p（ 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 ∩ O^p（ G） ｜ d.

关 键 词：基础数学 代数学 有限群 P-超可解 X-s-半置换 P-群 

分 类 号：O152.1[理学—数学]