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Groups whose proper subgroups have restricted infinite conjugacy classes

Volume 150 / 2017

Maria De Falco, Francesco de Giovanni, Mahmut Kuzucuoğlu, Carmela Musella Colloquium Mathematicum 150 (2017), 281-291 MSC: Primary 20F24. DOI: 10.4064/cm7015-1-2017 Published online: 29 September 2017

Abstract

A group $G$ is said to have the $\mathit{AFC} $-property if for each element $x$ of $G$ at least one of the indices $|G:C_G(x)|$ and $|C_G(x):\langle x\rangle|$ is finite. The class of $\mathit{AFC} $-groups, which generalize $\mathit{FC} $-groups, has been studied by De Falco et al. (2017) and Shalev (1994). Here the structure of groups whose proper subgroups have the $\mathit{AFC} $-property is investigated.

Authors

  • Maria De FalcoDipartimento di Matematica e Applicazioni
    Università di Napoli “Federico II”
    Napoli, Italy
    e-mail
  • Francesco de GiovanniDipartimento di Matematica e Applicazioni
    Università di Napoli “Federico II”
    Napoli, Italy
    e-mail
  • Mahmut KuzucuoğluDepartment of Mathematics
    Middle East Technical University
    Ankara, Turkey
    e-mail
  • Carmela MusellaDipartimento di Matematica e Applicazioni
    Università di Napoli “Federico II”
    Napoli, Italy
    e-mail

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