某些子群的半覆盖-远离性质对有限群结构的影响  

Influence of semi cover-avoiding subgroups on structure of finite group

作　　者：陈英宁 徐颖吾[1] 

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《哈尔滨商业大学学报（自然科学版）》2013年第6期743-745,共3页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：陕西省教育厅自然科学专项基金资助项目(11JK0499)

摘　　要：利用半覆盖-远离子群的性质研究了群的可解性和超可解性.研究了有限群G的极大子群具有可解半覆盖-远离性,给出了G为可解群的一个充要条件,利用有限群G的极大子群的半覆盖-远离性,得到了G为可解群的一个充分条件,讨论了G的Sylow子群的半覆盖-远离性质,得出了G为p可解的充分条件.In this paper, solvability and supersolvability of the finite group G were character- ized using the properties of semi cover - avoiding subgroups. A sufficient and necessary con- dition for solvability of the finite group G was given, using the solvability semi cover - avoi- ding properties of maximal subgroup of G, a sufficient condition for solvability of the finite group G was obtained, using the semi cover - avoiding properties of maximal subgroup of G, and a sufficient condition for p - solvability of the finite group G was obtained under the dis- cussion that Sylow subgroups of G have semi cover - avoiding properties.

关 键 词：CAP半子群 CAP子群 极大子群 可解群 超可解群 P-可解群 

分 类 号：O152[理学—数学]