We study the automorphisms of a graph product of finitely-generated abelian groups W . More precisely, we study a natural subgroup Aut W of AutW , with Aut W = AutW whenever vertex groups are finiteâ€¦ (More)

We show that if G is a group and G has a graphproduct decomposition with finitely-generated abelian vertex groups, then G has two canonical decompositions as a graph product of groups: a uniqueâ€¦ (More)

The present paper records more details of the relationship between primitive elements and palindromes in F2, the free group of rank two. We characterize the conjugacy classes of palindromic primitiveâ€¦ (More)

We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank twoâ€¦ (More)

In mathematics, a group is the set of symmetries of an object. Coxeter groups are a broad and natural class of groups that are related to reflectional symmetries. Each Coxeter group is determined byâ€¦ (More)

The issue of recognizing group properties, such as the cardinality of the group, directly from the dynamics of an incomplete coset enumeration is discussed. In particular, it is shown that theâ€¦ (More)

The centrepiece of this paper is a normal form for primitive elements which facilitates the use of induction arguments to prove properties of primitive elements. The normal form arises from anâ€¦ (More)

We characterize certain properties of the derived series of Coxeter groups by properties of the corresponding Coxeter graphs. In particular, we give necessary and sufficient conditions for a Coxeterâ€¦ (More)

We prove that the groups presented by finite convergent monadic rewriting systems with generators of finite order are exactly the free products of finitely many finite groups, thereby confirmingâ€¦ (More)

For n â‰¥ 2, the group of finite sequences of elementary Andrewsâ€“ Curtis transformations on the set of n-tuples is anti-isomorphic to a subgroup AC(n) of the automorphism group of a free group F ofâ€¦ (More)