2 citations · 2 across the 4 of their papers we have counts for
10 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…
Invariable generation of certain branch groups
Charles Garnet Cox, Anitha Thillaisundaram
Let be a group. Then is an invariable generating set of if every subset obtained from by replacing each element with a conjugate is also a generatin…
On the finite index subgroups of Houghton's groups
Charles Garnet Cox
An erratum has been added to resolve an issue raised by Professor Derek Holt. This appears after the original paper, and also includes two new results. Original abstract: Houghton'…
On the spread of infinite groups
Charles Garnet Cox
A group is -generated if every non-trivial element is part of a generating pair. In 2019, Donoven and Harper showed that many Thompson groups are -generated and p…
Invariable generation and the Houghton groups
Charles Garnet Cox
The Houghton groups are a family of infinite groups. In 1975 Wiegold showed that was invariably generated (IG) but was not. A natural question…
Invariable generation and wreath products
Charles Garnet Cox
Invariable generation is a topic that has predominantly been studied for finite groups. In 2014, Kantor, Lubotzky, and Shalev produced extensive tools for investigating invariable…