Free products in linear groups

Profinite Topologies in Free Products of Groups

Let H be an abstract group and let C be a variety of finite groups (i.e., a class of finite groups closed under taking subgroups, quotients and finite direct products); for example the variety of all finite p-groups, for a fixed prime p. Consider the smallest topology on H such that all the homomorphism H −→ C from H to any group C ∈ C (endowed with the discrete topology) is continuous. We refe...

Free Products of Absolute Galois Groups *

Groups assembled from free and direct products

Let A be the collection of groups which can be assembled from infinite cyclic groups using the binary operations free and direct product. These groups can be described in several ways by graphs. The group (Z ∗Z)×(Z ∗Z) has been shown by [1] to have a rich subgroup structure. In this article we examine subgroups of A–groups. DefineA to be the smallest class of groups which contains the infinite ...

Subgroups of Free Topological Groups and Free Topological Products of Topological Groups

Introduction Our objectives are topological versions of the Nielsen-Schreier Theorem on subgroups of free groups, and the Kurosh Theorem on subgroups of free products of groups. It is known that subgroups of free topological groups need not be free topological [2, 6, and 9]. However we might expect a subgroup theorem when a continuous Schreier transversal exists, and we give such a result in th...

The Conjugacy Problem in Wreath Products and Free Metabelian Groups

1. Introduction. The conjugacy problem was formulated by Dehn in 1912 for finitely presented groups [1]. The question was whether it can be effectively determined for such a group when two elements are conjugate. This general question was answered in the negative by Novikov in 1954 [6J. But it is still of interest to determine whether the problem is solvable for particular finitely presented gr...