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Profinite groups in which centralizers are abelian

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, University of Brasilia, 70910-900, Brasilia, Brazil

    Pavel Shumyatsky, Pavel Zalesskii & Theo Zapata

Authors
  1. Pavel Shumyatsky
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  2. Pavel Zalesskii
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  3. Theo Zapata
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Correspondence to Theo Zapata.

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To Alex Zalesski on the occasion of his 80th birthday

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Shumyatsky, P., Zalesskii, P. & Zapata, T. Profinite groups in which centralizers are abelian. Isr. J. Math. 230, 831–854 (2019). https://doi.org/10.1007/s11856-019-1838-x

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  • DOI: https://doi.org/10.1007/s11856-019-1838-x

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