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

### ON A CHARACTERIZATION OF QUASICYCLIC GROUPS

### Dabin Zheng, Yujie Ma and Heguo Liu

Faculty of Mathematics and Computer Science, Hu Bei University,
Wuhan 430062, Hubei Province, China

*e-mail:* `zhengdabin@mmrc.iss.ac.cn`
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.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.42.2.09

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MathSciNet

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