Geodesic
Classes of conjugate elements in finitary permutation groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 63-77

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We study the permutation properties of the conjugacy actions of a finitary permutation group on its classes of conjugate elements. These properties are used to show that classes of conjugate elements in finitary permutation groups are discrete subsets with respect to any Hausdorff group topology. Moreover, it is proved that the above property characterizes alternating groups in the class of countable locally finite simple groups.
Keywords: finitary permutation groups, unconditionally discrete sets
Mots-clés : minimal group topologies. 
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     author = {V. V. Belyaev},
     title = {Classes of conjugate elements in finitary permutation groups},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {63--77},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a7/}
}
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V. V. Belyaev. Classes of conjugate elements in finitary permutation groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 63-77. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a7/