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Keywords:

  • Residually finite groups;
  • profinite groups;
  • genus MSC (2010) 20E06;
  • 20E18

Abstract

We find a bound on the genus of an HNN-extension HNN(K, A, f) with a finite base group K. We also give sufficient conditions when the genus is 1, i.e. when HNN(K, A, f) is determined by its profinite completion up to isomorphism with respect to the family of all virtually free groups.