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A note on the power graphs of finite nilpotent groups

2020
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Filomat
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The power graph P(G) of a group G is the graph with vertex set G and two distinct vertices are adjacent if one is a power of the other. Two finite groups are said to be conformal, if they contain the same number of elements of each order. Let Y be a family of all non-isomorphic odd order finite nilpotent groups of class two or p-groups of class less than p. In this paper, we prove that the power graph of each group in Y is isomorphic to the power graph of an abelian group and two groups in Y

doi:10.2298/fil2007451j
fatcat:344sb6minvgh7ex75zuxvbuoyi