Finite groups are 1-isomorphic iff their directed power graphs are isomorphic

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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

Suppose G and H are Finite group (?)s. Then, G and H are 1-isomorphic groups (?) (in particular, 1-isomorphic finite groups (?)if and only if their directed power graphs are isomorphic as directed graphs.

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