This article is cited in 3 papers

A characterization of infinite Chernikov groups that are not finite extensions of quasi-cyclic groups

A. A. Shafiro, V. P. Shunkov


Abstract: We characterize the groups named in the title. Our main result is as follows: an infinite locally finite group $G$ that is not a finite extension of a quasi-cyclic group is a Chernikov group if and only if it has a subgroup $H$ of finite index whose holomorph contains a copy of the four-group in such a way that the centralizer in $H$ of each of its three involutions is a Chernikov group.
Bibliography: 17 titles.

UDC: 519.45

MSC: Primary 20E25; Secondary 20D05

Received: 26.01.1977 and 18.01.1978

 English version: Mathematics of the USSR-Sbornik, 1979, 35:4, 569–580

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