On the Diameters of Commuting Graphs of Permutational Wreath Products
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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 Open image in new window 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.
KeywordsMaximal Length Symmetric Group Permutation Group Cayley Graph Wreath Product
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- 2.M. Giudici and C. Parker, “There is no upper bound for the diameter of the commuting graph of a finite group,” arXiv 2012 (http://arxiv.org/abs/1210.0348v1).
- 6.G. L. Morgan and C. W. Parker, “The diameter of the commuting graph of a finite group with trivial centre,” arXiv 2013 (http://arxiv.org/abs/1301.2341v1).
- 7.M. Guidici and A. Pope, “On bounding the diameter of the commuting graph of a group,” arXiv 2012 (http://arxiv.org/abs/1206.3731).
- 11.I. M. Isaacs, Finite Group Theory [Graduate Studies in Mathematics, Vol. 92], AMS, Providence, RI (2008).Google Scholar
- 13.The GAP Group, GAP—Groups, Algorithms, and Programming, Version 4.6.3 (2013) (http://www.gap-system.org).
- 14.V. I. Sushchansky and V. S. Sikora, Operations on the Permutation Groups [in Ukrainian], Chernivtsi, Ruta (2003).Google Scholar