真商群为s-自对偶群的有限p-群  

Finite p-groups All of Whose Proper Quotient Groups Are s-self Dual

作　　者：李立莉 LI Lili(School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang,Guangdong,524048,P.R.China)

机构地区：[1]岭南师范学院数学与统计学院,广东湛江524048

出　　处：《数学进展》2021年第1期153-159,共7页Advances in Mathematics（China）

基　　金：Supported by NSFC (Nos.11701254,12061030);Education and Teaching Reform Project of Lingnan Normal University (No.LSJGYB1922);Key Subject Program of Lingnan Normal University (No.1171518004)。

摘　　要：如果有限群G的每个子群与G的某个商群同构,则称群G为s-自对偶群.如果s-自对偶群G的每个商群与G的某个子群同构,则称群G为自对偶群.本文分类了每个真商群均为s-自对偶群的有限p-群.作为推论,本文还分类了每个真截段均为s-自对偶群的有限p-群,每个真商群均为自对偶群的有限p-群,以及每个真截段均为自对偶群的有限p-群.A group G is s-self dual if every subgroup of G is isomorphic to a quotient group of G.A group G is self dual if G is s-self dual and every quotient group of G is isomorphic to a subgroup of G.In this article,finite p-groups all of whose proper quotient groups are s-self dual are classified.As a corollary,finite p-groups all of whose proper sections are s-self dual,finite p-groups all of whose proper quotient groups are self dual,and finite p-groups all of whose proper sections are self dual are also classified.

关 键 词：有限P-群 s-自对偶群 外s-自对偶群 

分 类 号：O152.1[理学—数学]