11 citations · 40 across the 16 of their papers we have counts for
16 papers
Conjugator length in finitely presented groups
Martin R. Bridson, Timothy R. Riley, Andrew W. Sale
The conjugator length function of a finitely generated group gives the minimal upper bound on the length of a conjugator for a pair of words that represent conjugate elements i…
Conjugacy in a family of free-by-cyclic groups
Martin R. Bridson, Timothy R. Riley, Andrew W. Sale
We analyse the geometry and complexity of the conjugacy problem in a family of free-by-cyclic groups where the defining free-group automorphism is positi…
On virtual indicability and property (T) for outer automorphism groups of RAAGs
Andrew Sale
We give a condition on the defining graph of a right-angled Artin group which implies its automorphism group is virtually indicable, that is, it has a finite-index subgroup that ad…
Calculating the virtual cohomological dimension of the automorphism group of a RAAG
Matthew B. Day, Andrew W. Sale, Richard D. Wade
We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right-angled Artin group. The algorithm works in the relative setting; in partic…
Outer automorphism groups of graph products: subgroups and quotients
Andrew Sale, Tim Susse
We show that the outer automorphism groups of graph products of finitely generated abelian groups satisfy the Tits alternative, are residually finite, their so-called Torelli subgr…
Outer automorphism groups of right-angled Coxeter groups are either large or virtually abelian
Andrew Sale, Tim Susse
We generalise the notion of a separating intersection of links (SIL) to give necessary and sufficient criteria on the defining graph of a right-angled Coxeter group so th…
Vastness properties of automorphism groups of RAAGs
Vincent Guirardel, Andrew Sale
Outer automorphism groups of RAAGs, denoted , interpolate between and . We consider several vastness properties for which behaves…
Metric Approximations of Wreath Products
Ben Hayes, Andrew Sale
Given the large class of groups already known to be sofic, there is seemingly a shortfall in results concerning their permanence properties. We address this problem for wreath prod…
The Wreath Product of Two Sofic Groups is Sofic
Ben Hayes, Andrew Sale
Given sofic approximations for countable, discrete groups , we construct a sofic approximation for their wreath product .
Permute and conjugate: the conjugacy problem in relatively hyperbolic groups
Yago Antolín, Andrew Sale
Modelled on efficient algorithms for solving the conjugacy problem in hyperbolic groups, we define and study the permutation conjugacy length function. This function estimates the…
The Geometry of the Conjugacy Problem in Wreath Products and Free Solvable Groups
Andrew W. Sale
We describe an effective version of the conjugacy problem and study it for wreath products and free solvable groups. The problem involves estimating the length of short conjugators…
Palindromic width of wreath products, metabelian groups, and max-n solvable groups
T. R. Riley, A. W. Sale
A group has finite palindromic width if there exists such that every element can be expressed as a product of or fewer palindromic words. We show that if has finite pal…
Bounded Conjugators For Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups
Andrew W. Sale
Let be a real semisimple Lie group with trivial centre and no compact factors. Given a conjugate pair of either real hyperbolic elements or unipotent elements and in $G…
Conjugacy Length in Group Extensions
Andrew W. Sale
Determining the length of short conjugators in a group can be considered as an effective version of the conjugacy problem. The conjugacy length function provides a measure for thes…
Metric Behaviour of the Magnus Embedding
Andrew W. Sale
The classic Magnus embedding is a very effective tool in the study of abelian extensions of a finitely generated group , allowing us to see the extension as a subgroup of a wrea…
The geometry of the conjugacy problem in lamplighter groups
Andrew W. Sale
In this note we investigate the conjugacy problem in lamplighter groups with particular interest in the role of their geometry. In particular we show that the conjugacy length func…