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Generalized FC-groups with chain conditions

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Abstract

Let c be a positive integer. A group G is called an FC c -group if each element of G has only finitely many conjugates by γc G, and γc G lies in the FC-center of G. The FC c -groups with the minimal condition or the maximal conditions on abelian subgroups are investigated and some characterizations of them are obtained. A group is called an FC c -soluble group if it possesses an FC c -series of finite length. Another aim of this article is to give necessary and sufficient conditions for FC c -soluble groups to satisfy the minimal condition or the maximal conditions on abelian subgroups.

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Authors and Affiliations

  1. School of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan, P. R. China

    Zh. Zhang & Sh. Chen

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  1. Zh. Zhang
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  2. Sh. Chen
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Correspondence to Zh. Zhang.

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Original Russian Text Copyright © 2015 Zhang Zh. and Chen Sh.

The authors were supported by the National Natural Foundation of P. R. China (Grants 11471055; 11371335).

Chengdu. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 4, pp. 934–941, July–August, 2015; DOI: 10.17377/smzh.2015.56.416.

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Zhang, Z., Chen, S. Generalized FC-groups with chain conditions. Sib Math J 56, 746–751 (2015). https://doi.org/10.1134/S0037446615040163

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  • DOI: https://doi.org/10.1134/S0037446615040163

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