Infinite Presentability Of Groups And Condensation

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.


Published in:
Journal Of The Institute Of Mathematics Of Jussieu, 13, 4, 811-848
Year:
2014
Publisher:
Cambridge, Cambridge Univ Press
ISSN:
1474-7480
Keywords:
Laboratories:




 Record created 2014-11-13, last modified 2018-03-17


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