The strong symmetric genus spectrum of nilpotent groups

Abstract

Let denote the set of positive integers that appear as the strong symmetric genus of a finite nilpotent group. We show that if g is not congruent to , then . Using this result and some abelian groups with genus congruent to , we establish a lower bound of 8/9 for the lower asymptotic density of the set . We also prove that there are an infinite number of positive integers not in the set .