# Same order statistics as abelian p-group not implies Lazard Lie group

From Groupprops

## Statement

It is possible to have two finite -groups and such that is abelian, and are order statistics-equivalent (i.e., and have the same order statistics), but is not a Lazard Lie group (?).

## Related facts

- Lazard Lie group has the same order statistics as the additive group of its Lazard Lie ring
- Finite abelian groups with the same order statistics are isomorphic
- Order statistics-equivalent not implies 1-isomorphic
- Finite group having the same order statistics as a cyclic group is cyclic

## Proof

There exist -groups of arbitrarily large nilpotency class and exponent .