16 citations · 42 across the 18 of their papers we have counts for
23 papers
Finiteness properties of Subgroups of Houghton Groups of full Hirsch length
Charles Garnet Cox, Peter Kropholler, Armando Martino
In the 1980's K.S. Brown proved that the Houghton group is of type but not . We show that, provided , the same conclusion…
Finiteness properties of stabilisers of oligomorphic actions
Francesco Fournier-Facio, Peter H. Kropholler, Robert Alonzo Lyman +1
An action of a group on a set is oligomorphic if it has finitely many orbits of -element subsets for all . We prove that for a large class of groups (including all groups of…
Coherence for elementary amenable groups
Sam Hughes, Dawid Kielak, Peter H. Kropholler +1
We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This genera…
The first -Betti number and groups acting on trees
Indira Chatterji, Sam Hughes, Peter Kropholler
We generalise results of Thomas, Allcock, Thom-Petersen, and Kar-Niblo to the first -Betti number of quotients of certain groups acting on trees by subgroups with free acti…
Isoperimetric inequalities for Poincaré duality groups
Dawid Kielak, Peter Kropholler
We show that every oriented -dimensional Poincaré duality group over a -ring is amenable or satisfies a linear homological isoperimetric inequality in dimension . As…
A property of the lamplighter group
Ilaria Castellano, Ged Corob Cook, Peter H. Kropholler
We show that the inert subgroups of the lamplighter group fall into exactly five commensurability classes. The result is then connected with the theory of totally disconnected loca…