`On p-groups of Gorenstein-Kulkarni type

A finite p-group is said to be of Gorenstein-Kulkarni type if the set of all elements of non-maximal order is a subgroup of index p. This notion is motivated from the fact that 2-groups of Gorenstein-Kulkarni type arise naturally in the study of group actions on compact Riemann surfaces. In this talk, we introduce the notions relevant to describe group actions on Riemann surfaces, in particular the notion of the genus spectrum of a finite group, show how the Gorenstein-Kulkarni property arises in this framework. We then proceed to towards a classification of groups of Gorenstein-Kulkarni type.