Journal article

Infinite presentability of groups and condensation

  • Bieri, Robert Department of Mathematics, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt am Main, Germany
  • Cornulier, Yves CNRS and Laboratoire de Mathématiques, Université Paris-Sud, France
  • Guyot, Luc STI, EPFL, Lausanne, Switzerland
  • Strebel, Ralph Département de Mathématiques, Fribourg, Switzerland
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  • Journal of the Institute of Mathematics of Jussieu. - 2014, vol. 13, no. 04, p. 811–848
English We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We introduce here a larger class of condensation groups, called infinitely independently presentable groups, and establish criteria which allow one to infer that a group is infinitely independently presentable. In addition, we construct examples of finitely generated groups with no minimal presentation, among them infinitely presented groups with Cantor–Bendixson rank 1, and we prove that every infinitely presented metabelian group is a condensation group.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
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