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On uniform permutations with finite dispersion parameters. (English. Russian original) Zbl 1308.20005

Proc. Steklov Inst. Math. 285, Suppl. 1, S163-S168 (2014); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 19, No. 3, 284-289 (2013).
Summary: We study the group \(G\) of uniform permutations of the set of integers with finite dispersion parameters. We prove that every finite subset of \(G\) lies in a subgroup of the form \(Q=AB\), where \(A\) and \(B\) are locally finitely approximable subgroups of \(G\).

MSC:

20B35 Subgroups of symmetric groups
20B07 General theory for infinite permutation groups
20F50 Periodic groups; locally finite groups
20E25 Local properties of groups
20E07 Subgroup theorems; subgroup growth
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