Israel Journal of Mathematics

, Volume 230, Issue 2, pp 831–854 | Cite as

Profinite groups in which centralizers are abelian

  • Pavel Shumyatsky
  • Pavel Zalesskii
  • Theo ZapataEmail author


The article deals with profinite groups in which the centralizers are abelian (CA-groups), that is, with profinite commutativity-transitive groups. It is shown that such groups are virtually pronilpotent. More precisely, let G be a profinite CA-group. It is shown that G has a normal open subgroup N which is either abelian or pro-p. Further, rather detailed information about the finite quotient G/N is obtained.


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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • Pavel Shumyatsky
    • 1
  • Pavel Zalesskii
    • 1
  • Theo Zapata
    • 1
    Email author
  1. 1.Department of MathematicsUniversity of BrasiliaBrasiliaBrazil

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