Rank and deficiency gradients of generalised Thompson groups of type F

Abstract

For an arbitrary sequence $(G_s)$ of subgroups of finite index in the generalised Thompson group $$F_{n,\infty }=⟨x_0,x_1,\dots ,x_m,\dots \mid x_i^{x_j}=x_{i+n-1}fori>j\ge 0⟩$$ it is shown that ${\sup }_{s\ge 1}d(G_s)<\infty$ and that the deficiency gradient of $F_{n,\infty }$ with respect to $(G_s)$ is 0 provided $[G:G_s]$ tends to infinity. A higher dimensional analogue is considered for $n=2$.

References in corpus (3)

• The chameleon groups of Richard J. Thompson: automorphisms and dynamics
• Automorphisms of generalized Thompson groups
• Deficiency and abelianized deficiency of some virtually free groups