Order-cum-power statistics-equivalent finite 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 finite groups are said to be order-cum-power statistics-equivalent if they have the same order-cum-power statistics functions.

Relation with other relations

Stronger relations

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
1-isomorphic groups (finite case) 1-isomorphic implies order-cum-power statistics-equivalent order-cum-power statistics-equivalent not implies 1-isomorphic

Weaker relations

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Order statistics-equivalent finite groups
Power statistics-equivalent finite groups