Undirected power graph-equivalent groups

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This article defines an equivalence relation over the collection of groups. View a complete list of equivalence relations on groups.

Definition

Two groups G and H are termed undirected power graph-equivalent groups if their undirected power graphs are isomorphic as graphs.

Relation with other relations

Stronger relations

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
isomorphic groups 1-isomorphic groups, Directed power graph-equivalent groups|FULL LIST, MORE INFO
1-isomorphic groups (via directed power graph-equivalent) (via directed power graph-equivalent) Directed power graph-equivalent groups|FULL LIST, MORE INFO
directed power graph-equivalent groups |FULL LIST, MORE INFO