Random subgroups of linear groups are free

Random Normal Subgroups of Free Profinite Groups

Fixed subgroups are compressed in free groups

In this paper we prove that the fixed subgroup of an arbitrary family of endomorphisms ψi, i ∈ I, of a finitely generated free group F , is F -super-compressed. In particular, r(∩i∈IFix ψi) ≤ r(M) for every subgroup M ≤ F containing ∩i∈IFix ψi. This provides new evidence towards the inertia conjecture for fixed subgroups of free groups. As a corollary, we show that, in the free group of rank n,...

Linear programming and the intersection of subgroups in free groups

We study the intersection of finitely generated subgroups of free groups by utilizing the method of linear programming. We prove that if H1 is a finitely generated subgroup of a free group F , then the Walter Neumann coefficient σ(H1) of H1 is rational and can be computed in deterministic exponential time of size of H1. This coefficient σ(H1) is a minimal nonnegative real number such that, for ...

Free Subgroups in Linear Groups and Group Rings

This paper is an extension of the talk I gave at the International Conference on Non-Commutative Rings, Group Rings, Diagram Algebras and Applications at the University of Madras in December 2006. It discusses certain techniques used to prove the existence of free subgroups in linear groups and in the unit group of integral group rings of finite groups. Its main focus is recent joint work with ...

Subgroups of Free Metabelian Groups

In 1954 A. G. Howson proved that the intersection of two finitely generated subgroups of a free group is again finitely generated. Now the free metabelian subgroups of a free metabelian group of finite rank n are quite restricted. Indeed they are again of finite rank at most n. This suggests that there may be an analog of Howson’s theorem for free metabelian groups. This turns out not to be the...