Separability and randomness in free groups

Subgroup Separability in Residually Free Groups

We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type FP∞ are virtual retracts. We describe a uniform solution to the membership problem for finitely presentable subgroups of residually free groups.

Randomness and Complexity in Matrix Groups

We reflect on how to define complexity of a matrix and how to sample a random invertible matrix. We also discuss a related issue of complexity of algorithms in matrix groups. In memory of Alfred Lvovich Shmelkin, a man of honor and integrity

Subgroup separability and virtual retractions of groups

We begin by recalling that if Γ is a group, andH a subgroup of Γ, then Γ is calledH-separable if for every g ∈ Γ\H, there is a subgroup K of finite index in Γ such that H ⊂ K but g / ∈ K. The group Γ is called subgroup separable (or LERF) if Γ is H-separable for all finitely generated subgroups H. As is well-known LERF is a powerful property in the setting of low-dimensional topology which has ...

On Subgroup Separability in Hyperbolic Coxeter Groups

Graphs and Separability Properties of Groups

Ž . A group G is LERF locally extended residually finite if for any finitely generated subgroup S of G and for any g f S there exists a finite index subgroup S of G which contains S but not g. Using graph-theoretical methods we give 0 algorithms for constructing finite index subgroups in amalgamated free products of groups with good separability properties. We prove that a free product of a fre...