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

Author(s): Yu. Yu. Leshchenko | L. V. Zoria

Journal: Carpathian Mathematical Publications
ISSN 2075-9827

Volume: 5;
Issue: 1;
Start page: 70;
Date: 2013;
Original page

Keywords: commuting graph | wreath product | Sylow $p$-subgroup | symmetric group

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