Splitting theorems for pro-p groups acting on pro-p trees

• Wolfgang Herfor ^[2] ; Pavel Zalesskii ^[1] ; Theo Zapata ^[1]
  1. [1] Universidade de Brasília

     Universidade de Brasília

     Brasil

     
  2. [2] University of Technology at Vienna
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 3, 2016, págs. 1245-1268
• Idioma: inglés
• DOI: 10.1007/s00029-015-0217-7
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• Resumen

  • Let G be an infinite finitely generated pro-p group acting on a pro-p tree such that the restriction of the action to some open subgroup is free. We prove that G splits over an edge stabilizer either as an amalgamated free pro-p product or as a pro-p HNNHNN -extension. Using this result, we prove under a certain condition that free pro-p products with procyclic amalgamation inherit from its amalgamated free factors the property of each 2-generated pro-p subgroup being free pro-p. This generalizes known pro-p results, as well as some pro-p analogues of classical results in abstract combinatorial group theory.