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