Conformality and p-isomorphism in finite nilpotent groups

Abstract

This paper discusses the relationship between two equivalence relations on the class of finite nilpotent groups. Two finite groups are conformal if they have the same number of elements of all orders. (Notation: G ≈ H.) This relation is discussed in [4] pp 107–109 where it is shown that conformality does not necessarily imply isomorphism, even if one of the groups is abelian. However, if both groups are abelian the position is much simpler. Finite conformal abelian groups are isomorphic.