| 真商群为s-自对偶群的有限p-群 |
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| 引用本文： | 李立莉.真商群为s-自对偶群的有限p-群[J].数学进展,2021(1):153-159. |
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| 作者姓名： | 李立莉 |
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| 作者单位： | 岭南师范学院数学与统计学院 |
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| 基金项目： | 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)。 |
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| 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.
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| 关 键 词： | 有限P-群 s-自对偶群 外s-自对偶群 |
Finite p-groups All of Whose Proper Quotient Groups Are s-self Dual |
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| LI Lili.Finite p-groups All of Whose Proper Quotient Groups Are s-self Dual[J].Advances in Mathematics,2021(1):153-159. |
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| Authors: | LI Lili |
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| Institution: | (School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang,Guangdong,524048,P.R.China) |
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| Abstract: | 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. |
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| Keywords: | finite p-groups s-self dual groups outer s-self dual groups |
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