子群指数给出的超可解群的一个充要条件  

A Necessary and Sufficient Condition of Supersolvable Group Offered by Index of Subgroup

作　　者：曾利江[1] 

机构地区：[1]遵义师范学院数学系,贵州遵义563002

出　　处：《河南大学学报（自然科学版）》2010年第2期119-121,共3页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(21679102);贵州省教育厅自然科学资助基金(黔教科2007069);贵州省科技厅自然科学资助基金(黔科合J字[2009]2075号)

摘　　要：首先证明了如果群G有一个正规循环子群H,使对应的商群G/H是超可解的,则G本身必定是超可解群;然后证明了G的子群H有一切可能指数的子群,当且仅当它有一切可能素指数的子群,最后证明了群G为超可解当且仅当它的每个子群含有指数为任意素数的子群.This paper proved first that group G itself must be supersolvable group if G has a normal cyclic subgroup H and the corresponding quotient group G/H should be supersolvable; Then, proved that subgroup H of G has all subgroups with possible index if it has all subgroups with possible prime index; Finally, proved that G should be supersolvable if every subgroup has the index with arbitrary prime number.

关 键 词：超可解群 正规循环子群 主因子 主群列 

分 类 号：O152[理学—数学]