Order-cum-power statistics-equivalent finite groups
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 |