Classification of Finite Group Automorphisms with a Large Cycle
Alexander Bors · Communications in Algebra · 2016
The investigation of finite groups classifying as “extreme” according to certain quantitative conditions has a long history. The aim of this paper is to classify the pairs (G, α) where G is a finite group and α is an automorphism of G with a cycle of length greater than . In particular, it is shown that every finite group G having such an automorphism is abelian.