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Abstract
The directed power graph of a group G is the digraph with vertex set G, having an arc from y to x whenever x is a power of y; the undirected power graph has an edge joining x and y whenever one is a power of the other. We show that, for a finite group, the undirected power graph determines the directed power graph up to isomorphism. As a consequence, two finite groups which have isomorphic undirected power graphs have the same number of elements of each order.
Received: 2010-01-04
Published Online: 2010-05-30
Published in Print: 2010-November
© de Gruyter 2010
