Glasnik Matematicki, Vol. 42, No.2 (2007), 357-362.

ON A CHARACTERIZATION OF QUASICYCLIC GROUPS

Dabin Zheng, Yujie Ma and Heguo Liu

KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
e-mail: yjma@mmrc.iss.ac.cn

Faculty of Mathematics and Computer Science, Hu Bei University, Wuhan 430062, Hubei Province, China
e-mail: liuheguo0@163.com

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).

2000 Mathematics Subject Classification.   20E18, 20F16, 20E34.

Key words and phrases.   Quasicyclic group, hypo-inner Σ group, commutator subgroup, solvable group.

DOI: 10.3336/gm.42.2.09

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