On Groups in Which Many Automorphisms Are Cyclic.

Let G be a group. An automorphism α of G is said to be a cyclic automorphism if the subgroup 〈 x , x α 〉 is cyclic for every element x of G. In [F. de Giovanni, M.L. Newell, A. Russo: On a class of normal endomorphisms of groups, J. Algebra and its Applications 13, (2014), 6pp] the authors proved that every cyclic automorphism is central, namely, that every cyclic automorphism acts trivially on the factor group G / Z (G) . In this paper, the class F W of groups in which every element induces by conjugation a cyclic automorphism on a (normal) subgroup of finite index will be investigated. [ABSTRACT FROM AUTHOR]