2017
Том 69
№ 7

All Issues

On the Diameters of Commuting Graphs of Permutational Wreath Products

Leshchenko Yu. Yu.

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Abstract

Let G be a group and let Z(G) be the center of G. The commuting graph of the group G is an undirected graph Γ(G) with the vertex set G \ Z(G) such that two vertices x, y are adjacent if and only if xy = yx. We study the commuting graphs of permutational wreath products H G, where G is a transitive permutation group acting on X (the top group of the wreath product) and (H, Y) is an Abelian permutation group acting on Y.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 5, pp 732-742.

Citation Example: Leshchenko Yu. Yu. On the Diameters of Commuting Graphs of Permutational Wreath Products // Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 656–665.

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