Classification of skew morphisms of cyclic groups which are square roots of automorphisms

Abstract

The auto-index of a skew morphism φ of a finite group A is the smallest positive integer h such that φ^h is an automorphism of A. In this paper we develop a theory of auto-index of skew morphisms, and as an application we present a complete classification of skew morphisms of finite cyclic groups which are square roots of automorphisms.