C. Cox

collaborators

3 papers

math.GR2026

A note on the $R_{\infty}$ property for groups $FAlt (X) ⩽ G ⩽ Sym (X)$

Charles Garnet Cox

Given a set $X$ , the group $Sym (X)$ consists of all bijections from $X$ to $X$ , and $FSym (X)$ is the subgroup of maps with finite support i.e. those that move onl…

math.GR2026

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 $H_{n}$ is of type $F_{n - 1}$ but not $FP_{n}$ . We show that, provided $n \geq 3$ , the same conclusion…

math.GR2025

Invariable generation of certain branch groups

Charles Garnet Cox, Anitha Thillaisundaram

Let $G$ be a group. Then $S \subseteq G$ is an invariable generating set of $G$ if every subset $S^{'}$ obtained from $S$ by replacing each element with a conjugate is also a generatin…

A note on the R∞​ property for groups FAlt(X)⩽G⩽Sym(X)

Finiteness properties of Subgroups of Houghton Groups of full Hirsch length

Invariable generation of certain branch groups

A note on the $R_{\infty}$ property for groups $FAlt (X) ⩽ G ⩽ Sym (X)$