On Hypercentral Groups G With |G:G n |<∞ |
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| Authors: | Lv Heng Zeyong Duan Guiyun Chen |
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| Institution: | 1. College of Mathematics and Finance , Southwest China University , ChongQing, China lvh529@sohu.com;3. Department of Computation Science , Chengdu University of Information Technology , Chengdu, China;4. College of Mathematics and Finance , Southwest China University , ChongQing, China |
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| Abstract: | In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G p |<∞ (of course, it contains G = G p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞. |
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| Keywords: | Divisible Abelian groups Hypercentral groups Radicable groups Semi-radicable groups |
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