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Groups with finitary classes of conjugate elements

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Abstract

A class of conjugate elements of a group is called finitary if the conjugation action of the group induces a group of finitary permutations of this class. A group with finitary classes of conjugate elements will be called a ΦC-group. Some characterizations of ΦC-groups in the class of all groups have been obtained. It is also shown for every ΦC-group that either it is an FC-group, i.e., a group with finite classes of conjugate elements, or its structure is close to the structure of a totally imprimitive group of finitary permutations.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, per. Institutskii 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    V. V. Belyaev

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  1. V. V. Belyaev
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Correspondence to V. V. Belyaev.

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Original Russian Text © V.V. Belyaev, 2013, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Vol. 19, No. 3.

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Belyaev, V.V. Groups with finitary classes of conjugate elements. Proc. Steklov Inst. Math. 285 (Suppl 1), 42–57 (2014). https://doi.org/10.1134/S0081543814050058

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  • DOI: https://doi.org/10.1134/S0081543814050058

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