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On Groups in Which Many Automorphisms Are Cyclic

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mattia Brescia & Alessio Russo, 2022. "On Groups in Which Many Automorphisms Are Cyclic," Mathematics, MDPI, vol. 10(2), pages 1-7, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:262-:d:725698
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