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Original scientific paper

https://doi.org/10.3336/gm.42.2.09

On a characterization of quasicyclic groups

Dabin Zheng ; Faculty of Mathematics and Computer Science, Hu Bei University, Wuhan 430062, Hubei Province, China
Yujie Ma ; KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Heguo Liu ; Faculty of Mathematics and Computer Science, Hu Bei University, Wuhan 430062, Hubei Province, China


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Abstract

Let G be an infinite solvable group (resp. an infinite group properly containing its commutator subgroup G'). We prove that G is isomorphic to a quasicyclic group if and only if all proper normal subgroups of G are finitely generated (resp. all proper normal subgroups of G are cyclic or finite).

Keywords

Quasicyclic group, hypo-inner Σ group, commutator subgroup, solvable group

Hrčak ID:

17947

URI

https://hrcak.srce.hr/17947

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