Engel-like conditions in fixed points of automorphisms of profinite groups

  • Cristina AcciarriEmail author
  • Danilo Silveira


Let q be a prime and A an elementary abelian q-group acting as a coprime group of automorphisms on a profinite group G. We show that if A is of order \(q^2\) and some power of each element in \(C_G(a)\) is Engel in G for any \(a\in A^{\#}\), then G is locally virtually nilpotent. Assuming that A is of order \(q^3\), we prove that if some power of each element in \(C_G(a)\) is Engel in \(C_G(a)\) for any \(a\in A^{\#}\), then G is locally virtually nilpotent. Some analogues of quantitative nature for finite groups are also obtained.


Profinite groups Automorphisms Centralizers Engel-like conditions 

Mathematics Subject Classification

Primary 20E18 20E36 Secondary 20F45 20F40 20D45 20F19 



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© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BrasiliaBrasília-DFBrazil
  2. 2.Department of MathematicsFederal University of GoiásCatalãoBrazil

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