SOME RESULTS ON n-CAMINA PAIRS OF GROUPS

Abstract

In [6], Lewis found a bound for|Z(G)| in terms of [G : Z(G)] where (G,Z(G)) is an Camina pair of groups.  In this paper we generalize this concept to n-Camina pairs of groups with respect to the variety of nilpotent groups of class at most n, and find a bound for \(\left|\frac{Z_n(G)}{Z_n-1(G)}\right|\) where (G,Z_n(G)) is an n-Camina pair of groups and G is a finite p-group.