Finite p-Groups All of Whose Proper Quotient Groups are Abelian or Inner-Abelian |
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| Authors: | Qinhai Zhang Lili Li Mingyao Xu |
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| Institution: | 1. Department of Mathematics , Shanxi Normal University , Linfen, Shanxi, China zhangqh@dns.sxnu.edu.cn;3. Department of Mathematics , Shanxi Normal University , Linfen, Shanxi, China |
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| Abstract: | In this article, finite p-groups all of whose proper quotient groups are abelian or inner-abelian are classified. As a corollary, finite p-group all of whose proper quotient groups are abelian, and finite p-groups all of whose proper sections are abelian or inner-abelian are also classified. |
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| Keywords: | Extraspecial p-groups Inner abelian p-groups Metacyclic p-groups Minimal non-abelian p-groups Outer abelian p-groups p-groups of maximal class |
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