Geodesic
Groups with finitary classes of conjugate elements
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 45-61
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A class of conjugate elements of a group is called finitary if the action of group by conjugation induces a group of finitary permutations of this class. A group with finitary classes of conjugate elements will be called a ФC-group. Some characterizations of ФC-groups in the class of all groups are obtained. It is also shown for every ФC-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.
Keywords: finitary permutation groups, generalized FC-groups. 
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V. V. Belyaev. Groups with finitary classes of conjugate elements. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 45-61. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a4/

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