On Groups in Which Many Automorphisms Are Cyclic

Mattia Brescia and Alessio Russo
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Mattia Brescia: Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, 80138 Napoli, Italy
Alessio Russo: Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, 81100 Caserta, Italy

Mathematics, 2022, vol. 10, issue 2, 1-7

Abstract: 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.

Keywords: FC-groups; FW-groups; cyclic automorphisms; cyclicizer (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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