RESEARCH ARTICLE

Conjugacy in finite state wreath powers of finite permutation groups

Andriy Oliynyk^a, Andriy Russyev<sup>b

a</sup> Taras Shevchenko National University of Kyiv, Volodymyrska 60, Kyiv, Ukraine, 01033
^b Department of Mathematics, National University of Kyiv-Mohyla Academy, Skovorody St. 2, Kyiv, Ukraine, 04070

Abstract: It is proved that conjugated periodic elements of the infinite wreath power of a finite permutation group are conjugated in the finite state wreath power of this group. Counter-examples for non-periodic elements are given.

Keywords: permutation group, wreath power, automorphism of a rooted tree, conjugacy.

MSC: 20E08, 20E06, 20F65

Received: 29.01.2019
Revised: 28.02.2019

Language: English