Undirected power graph determines directed power graph for finite group

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This article gives a proof/explanation of the equivalence of multiple definitions for the term 1-isomorphic finite groups
View a complete list of pages giving proofs of equivalence of definitions

Statement

For a finite group, the isomorphism class of its undirected power graph determines the isomorphism class of its directed power graph. In particular, since the directed power graph determines a finite group up to 1-isomorphism, the undirected power graph also determines the group up to 1-isomorphism. In other words, if two finite groups have isomorphic undirected power graphs, they are 1-isomorphic groups.

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