超可解正规子群之积仍是超可解的条件  

The Condition that Product of Two Supersolvable Normal Subgroups be Still Supersolvable Subgroups

作　　者：曾利江[1] 李湘 汤小燕 ZENG Lijiang;LI Xiang;TANG Xiaoyan(Northern Guizhou Institute of Culture and Economy,Zunyi Normal College,Zunyi 563000,Guizhou,China;Mathematics College,Zunyi Normal College,Zunyi 563000,Guizhou,China)

机构地区：[1]遵义师范学院黔北文化与经济研究院,贵州遵义563000 [2]遵义师范学院数学学院,贵州遵义563000

出　　处：《山西师范大学学报（自然科学版）》2023年第1期17-22,共6页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：遵义师范学院教务处资助课题(JGPY2021043)。

摘　　要：很多文献说明了超可解子群研究的重要性,由于两个超可解正规子群的积不一定是超可解群,保持两个超可解正规子群的积仍然是超可解群的条件,就值得去研究.引进p-主因子,强p-闭群等概念,证明了一些引理,逐步推导证明,最后得到了超可解正规子群的积仍是超可解的条件,即G′=[G,G]为幂零群.It is very important to study supersolvable subgroups by a lot of literature.Since the product of two supersolvable normal subgroup may not necessarily be supersolvable group,it is worth to study the conditions keep the product of two supersolvable normal subgroup still supersolvable subgroup.Introduce new concepts of pprincipal divisor,strictly p-closed group and so on.To show some lemma and article has been deduced step by step.The conditions are finally obtained product of two supersolvable normal subgroup be still supersolvable subgroups,namely the G'=[G,G]is nilpotent group.

关 键 词：p-主因子 强p-闭群 超可解群 SYLOW塔 

分 类 号：O152[理学—数学]