On p-groups of Gorenstein-Kulkarni type

TL;DR

This paper investigates finite p-groups of Gorenstein-Kulkarni type, focusing on their classification and natural occurrence in the context of group actions on compact Riemann surfaces.

Contribution

It advances the understanding of Gorenstein-Kulkarni p-groups by working towards their classification and exploring their role in geometric group actions.

Findings

Identification of properties characterizing Gorenstein-Kulkarni p-groups

Connection established between these groups and actions on Riemann surfaces

Progress towards a comprehensive classification of such p-groups

Abstract

A finite p-group is said to be of Gorenstein-Kulkarni type if the set of all elements of non-maximal order is a maximal subgroup. 2-groups of Gorenstein-Kulkarni type arise naturally in the study of group actions on compact Riemann surfaces. In this paper, we proceed towards a classification of p-groups of Gorenstein-Kulkarni type.