# Order-cum-power statistics-equivalent finite groups

From Groupprops

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 |