33 citations · 168 across the 48 of their papers we have counts for
8 papers · 1 filter
The stable Andrews-Curtis conjecture and thickenable presentations of the trivial group
Marc Lackenby
We establish an explicit upper bound on the number of stable Andrews-Curtis moves that convert thickenable balanced presentations of the trivial group to the standard one-generator…
Every finite group admits a just finite presentation
Marc Lackenby
A finite presentation < X | R > of a finite group is called `just finite' if removing any relation from R results in a presentation for an infinite group. It has been an open quest…
Detecting large groups
Marc Lackenby
Let G be a finitely presented group, and let p be a prime. Then G is 'large' (respectively, 'p-large') if some normal subgroup with finite index (respectively, index a power of p)…
Adding high powered relations to large groups
Marc Lackenby
A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. The main theorem of the paper is as follows. Let G be a fi…
New lower bounds on subgroup growth and homology growth
Marc Lackenby
We establish new strong lower bounds on the (subnormal) subgroup growth of a large class of groups. This includes the fundamental groups of all finite-volume hyperbolic 3-manifolds…
Large groups, Property (tau) and the homology growth of subgroups
Marc Lackenby
We investigate the homology of finite index subgroups G_i of a given finitely presented group G. Specifically, we examine d_p(G_i), which is the dimension of the first homology of…