TY - EJOUR
DO - 10.1017/S1474748013000327
AB - 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.
T1 - Infinite Presentability Of Groups And Condensation
IS - 4
DA - 2014
AU - Bieri, Robert
AU - Cornulier, Yves
AU - Guyot, Luc
AU - Strebel, Ralph
JF - Journal Of The Institute Of Mathematics Of Jussieu
SP - 811-848
VL - 13
EP - 811-848
PB - Cambridge Univ Press
PP - Cambridge
ID - 203206
KW - Cantor-Bendixson rank
KW - condensation group
KW - infinitely presented metabelian group
KW - invariant Sigma
KW - Thompson's group F
KW - space of marked groups
SN - 1474-7480
ER -