On diameters estimations of the commuting graphs of Sylow $p$-subgroups of the symmetric groups

  • Yu.Yu. Leshchenko Bogdan Khmelnytsky Cherkasy National University, 81 Shevchenka blvd., 18031, Cherkasy, Ukraine
  • L.V. Zoria Bogdan Khmelnytsky Cherkasy National University, 81 Shevchenka blvd., 18031, Cherkasy, Ukraine
Keywords: commuting graph, wreath product, Sylow $p$-subgroup, symmetric group
Published online: 2013-06-20

Abstract


The commuting graph of a group $G$ is an undirected graph whose vertices are non-central elements of $G$ and two distinct vertices $x,y$ are adjacent if and only if $xy=yx$. This article deals with the properties of the commuting graphs of Sylow $p$-subgroups of the symmetric groups. We define conditions of connectedness of respective graphs and give estimations of the diameters if graph is connected.

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How to Cite
(1)
Leshchenko Y., Zoria L. On Diameters Estimations of the Commuting Graphs of Sylow $p$-Subgroups of the Symmetric Groups. Carpathian Math. Publ. 2013, 5 (1), 70-78.