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Groups with finitary classes of conjugate elements. (English. Russian original) Zbl 1314.20029

Proc. Steklov Inst. Math. 285, Suppl. 1, S42-S57 (2014); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 19, No. 3, 45-61 (2013).
Summary: 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 \(\Phi\)C-group. Some characterizations of \(\Phi\)C-groups in the class of all groups have been obtained. It is also shown for every \(\Phi\)C-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.

MSC:

20F24 FC-groups and their generalizations
20E45 Conjugacy classes for groups
20B07 General theory for infinite permutation groups
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References:

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