Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

M Akhavan-Malayeri, دانشگاه الزهرا، دانشکده علوم گروه ریاضی
2016 Pizhūhish/hā-yi riyāz̤ī  
In this article we will find necessary and sufficient conditions for a fixed point free automorphism (fpf automorphism) of a group to be a commuting automorphism. For a given prime we find the smallest order of a non abelian p-group admitting a commuting fixed point free automorphism. We prove that a group of order p 3 having a commuting fpf automorphism, has a restricted structure. Moreover, we prove that if a finite group admits a fpf automorphism of order 4, then the converse of Laffey's
more » ... rse of Laffey's result holds in G 1 .
doi:10.29252/mmr.2.1.1 fatcat:tawzyqxsqjfkrci5aqpfwar7va