Free bases for normal subgroups of free groups

Random Normal Subgroups of Free Profinite Groups

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...

Lifting Free Subgroups of PSL(2, R) to Free Groups

Let F = 〈a, b〉 be a rank two free group, let G = 〈A,B〉 be a two generator subgroup of PSL(2,R) and let ρ be a faithful representation of F with ρ(a) = A and ρ(b) = B. If G is discrete and free, many results about the primitive elements of G are proved using the geometry that G inherits from PSL(2,R), the group of orientation preserving isometries of the hyperbolic plane. Some of these results c...

Classifying fuzzy normal subgroups of finite groups

In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though...