关于极大子群指数的一个注记Ⅱ  

A Note on Indices of Maximal Subgroups Ⅱ

作　　者：史江涛[1] 张翠[1] SHI Jiang-tao ZHANG Cui(School of Mathematics and Information Sciences, Yantai University, Yantai 264005, Chin)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2016年第4期235-237,共3页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11201401;11201403;11361075;11561021)

摘　　要：设G为有限群,满足对于G的每个奇数阶Sylow子群P,均有或者P正规于G或者G的包含NG(P)的极大子群有素数指数.本文证明了这类群G必有超可解型Sylow塔,改进了相关已知结果.不运用Thompson子群和Glauberman-Thompson定理,本文给出了非幂零极大子群指数皆为素数的有限群可解的一个不同的证明.Let G be a finite group such that for every Sylow subgroup P of G of odd order we have that P is normal in G or every maximal subgroup of G that contains NG （P） has prime index. We prove that such a group G must have a Sylow tower of supersolvable type, which improves a known result. Moreover, without applying Thompson- subgroup and Glauberman-Thompson theorem we give a distinct proof of the solvability of finite groups in which all non-nilpotent maximal subgroups have primes indices.

关 键 词：极大子群 非幂零极大子群 素数指数 超可解型Sylow塔 可解群 

分 类 号：O152.1[理学—数学]