On conjugacy classes in groups

Marcel Herzog, Patrizia Longobardi*, Mercede Maj

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let G be a group. Write G=G﹨{1}. An element x of G will be called deficient if 〈x〉<CG(x) and it will be called non-deficient if 〈x〉=CG(x). If x∈G is deficient (non-deficient), then the conjugacy class xG of x in G will be also called deficient (non-deficient). Let j be a non-negative integer. We shall say that the group G has defect j, denoted by G∈D(j) or by the phrase “G is a D(j)-group”, if exactly j non-trivial conjugacy classes of G are deficient.

Original languageEnglish
Pages (from-to)112-131
Number of pages20
JournalJournal of Algebra
StatePublished - 1 Jan 2024


  • Centralizers
  • Conjugacy classes
  • Locally graded groups


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