A study of the genus of a group

Abstract

In this paper, we improve the upper bounds for the genus of the group A = Z(m1) x Z(m2) x Z(m3) (in canonical form) with at least one even mi, i = 1,2,3. As a special case, our results reproduce the known results in the cases m(3) = 3 or both ms and ms are equal to 3.