Free products of topological groups with amalgamation

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...

Free Products with Amalgamation and 3-manifolds

Free Boolean Topological Groups

Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.

Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups

We consider random walks on the set of all words over a finite alphabet such that in each step only the last two letters of the current word may be modified and only one letter may be adjoined or deleted. We assume that the transition probabilities depend only on the last two letters of the current word. Furthermore, we consider also the special case of random walks on free products by amalgama...

On the Existence of Free Topological Groups

Given a Tychonoff space X and classes U and V of topological groups, we say that a topological group G = G(X, U, V) is a free (U, V)-group over X if (a) X is a subspace of G, (b) GE U, and (c) every continuous f:X+ H with H EV extends uniquely to a continuous homomorphism _?: G + H. For certain classes U and V, we consider the question of the existence of free (U, V)groups. Our principal result...