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CC-groups with periodic central factor

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Abstract

A group G is said to be a group with Černikov conjugacy classes or a CC-group if it induces on the normal closure of each one of its elements a group of automorphisms which is a Černikov group, that is, a finite extension of an abelian group satisfying the minimal condition on subgroups. This concept is a natural extension of that an FC-group, that is, a group in which every element has a finite number of conjugates. It is known that if G is an FC-group then the central factor G/Z(G) is periodic. This result does not hold for CC-groups and in this paper we study CC-groups G in which the central factor G/Z(G) is periodic, a finiteness condition which has a deep influence on the structure of the group G. In particular, we characterize those CC-groups as above that are FC-groups by imposing some additional conditions on their structure.

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Authors and Affiliations

  1. Departamento de Matemáticas Facultad de Ciencias, Universidad de Zaragoza, 50009, Zaragoza, Spain

    Miguel González, Javier Otal & Juan Manuel Peña

  2. Departamento de Matemática Aplicada EUITI, Universidad de Zaragoza, 50009, Zaragoza, Spain

    Miguel González, Javier Otal & Juan Manuel Peña

Authors
  1. Miguel González
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  2. Javier Otal
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  3. Juan Manuel Peña
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Additional information

This research has been supported by DGICYT (Spain) PS88-0085

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González, M., Otal, J. & Peña, J.M. CC-groups with periodic central factor. Manuscripta Math 69, 93–105 (1990). https://doi.org/10.1007/BF02567914

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  • DOI: https://doi.org/10.1007/BF02567914

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