有限群的σ半次正规子群  

Onσ-Semisubnormal Subgroups of Finite Groups

作　　者：郑毅 吴珍凤 殷霞[1] 杨南迎[1] ZHENG Yi;WU Zhenfeng;YIN Xia;YANG Nanying(School of Science, Jiangnan University, Wuxi Jiangsu 214122, China)

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《西南师范大学学报（自然科学版）》2022年第7期14-20,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：中央高校基本科研业务费专项资金项目(JUSRP121048).

摘　　要：令G是一个有限群.如果G中存在子群K,满足G=HK,且对任一K_(1)<K有HK_(1)<G,则称H在G中是半正规的.本文结合子群的σ次正规性和半正规性引入了新的子群概念.如果群G的子群H在G中是σ次正规的或者半正规的,则称H在G中是σ半次正规的.通过研究群G的完全Hallσ集中的子群及其极大子群的σ半次正规性,给出了G是σ可解群和超可解群的若干新的判别准则.G is a finite Group.A subgroup H of G is said to be seminormal in G if there is a subgroup K in G such that G=HK and the product HK_(1) is a proper subgroup of G for any subgroup K_(1) in K which differs from K.In this paper,a new concept of subgroups is introduced by combining theσ-subnormality and seminormality of subgroups.A subgroup H of G is calledσ-semisubnormal in G,if H isσ-subnormal in G or seminormal in G.By studying theσ-seminormality of subgroups and their maximal subgroups in the complete Hall set of typeσof G,some new criteria for G to be solvable group and supersolvable group are given.

关 键 词：有限群 半正规子群 σ次正规子群 σ半次正规子群 

分 类 号：O152.1[理学—数学]