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

From Groupprops

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