Alex Evetts
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View article: Conjugacy Class Growth in Virtually Abelian Groups
Conjugacy Class Growth in Virtually Abelian Groups Open
We study the conjugacy class growth function in finitely generated virtually abelian groups. That is, the number of elements in the ball of radius $n$ in the Cayley graph which intersect a fixed conjugacy class. In the class of virtually a…
View article: Twisted conjugacy growth series of virtually abelian groups
Twisted conjugacy growth series of virtually abelian groups Open
We initiate the study of the \emph{twisted conjugacy growth series} of a finitely generated group, the formal power series associated to the twisted conjugacy growth function. Our main result is that, for a virtually abelian group, this se…
View article: Rational sets in virtually abelian groups: Languages and growth
Rational sets in virtually abelian groups: Languages and growth Open
In this paper, we generalise and unify the results and methods used by Benson, Liardet, Evetts, and Evetts &Levine to show that rational sets in a virtually abelian group G have rational (relative) growth series with respect to any generat…
View article: Conjugacy Class Growth in Virtually Abelian Groups
Conjugacy Class Growth in Virtually Abelian Groups Open
We study the conjugacy class growth function in finitely generated virtually abelian groups. That is, the number of elements in the ball of radius $n$ in the Cayley graph which intersect a fixed conjugacy class. In the class of virtually a…
View article: Effective equation solving, constraints and growth in virtually abelian groups
Effective equation solving, constraints and growth in virtually abelian groups Open
In this paper we study the satisfiability and solutions of group equations when combinatorial, algebraic and language-theoretic constraints are imposed on the solutions. We show that the solutions to equations with length, lexicographic or…
View article: Using edt0l systems to solve some equations in the solvable Baumslag-Solitar groups
Using edt0l systems to solve some equations in the solvable Baumslag-Solitar groups Open
We investigate the solution sets to equations in the solvable Baumslag-
\nSolitar groups BS(1, k), k ≥ 2, and show that these sets are represented
\nby edt0l languages in some cases. In particular, we prove that
\nthe multiplication table …
View article: Conjugacy growth in the higher Heisenberg groups
Conjugacy growth in the higher Heisenberg groups Open
We calculate asymptotic estimates for the conjugacy growth function of finitely generated class 2 nilpotent groups whose derived subgroups are infinite cyclic, including the so-called higher Heisenberg groups. We prove that these asymptoti…
View article: Rational sets in virtually abelian groups: languages and growth
Rational sets in virtually abelian groups: languages and growth Open
In this paper we generalise and unify the results and methods used by Benson, Liardet, Evetts, and Evetts & Levine, to show that rational sets in a virtually abelian group G have rational (relative) growth series with respect to any genera…
View article: Using EDT0L systems to solve some equations in the solvable Baumslag-Solitar groups
Using EDT0L systems to solve some equations in the solvable Baumslag-Solitar groups Open
We investigate the solution sets to equations in the solvable Baumslag-Solitar groups $BS(1,k)$, $k\geq2$, and show that these sets are represented by EDT0L languages in some cases. In particular, we prove that the multiplication table of …
View article: Conjugacy growth in the higher Heisenberg groups
Conjugacy growth in the higher Heisenberg groups Open
We calculate asymptotic estimates for the conjugacy growth function of finitely generated class 2 nilpotent groups whose derived subgroup is infinite cyclic, including the so-called higher Heisenberg groups. We prove that these asymptotics…
View article: Equations in virtually abelian groups: languages and growth
Equations in virtually abelian groups: languages and growth Open
This paper explores the nature of the solution sets of systems of equations in virtually abelian groups. We view this question from two angles. From a formal language perspective, we prove that the set of solutions to a system of equations…
View article: Rational growth in virtually abelian groups
Rational growth in virtually abelian groups Open
We show that any subgroup of a finitely generated virtually abelian group $G$ grows rationally relative to $G$, that the set of right cosets of any subgroup of $G$ grows rationally, and that the set of conjugacy classes of $G$ grows ration…
View article: The conjugacy growth of the soluble Baumslag-Solitar groups
The conjugacy growth of the soluble Baumslag-Solitar groups Open
In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups $BS(1,k)$, $k\geq 2$, with respect to the standard generating set, by providing a complete description of geodesic conjugacy representatives.…
View article: The conjugacy growth of the soluble Baumslag-Solitar groups
The conjugacy growth of the soluble Baumslag-Solitar groups Open
In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups BS(1, k) k ≥ 2, with respect to the standard generating set, by providing a complete description of geodesic conjugacy representatives. We sh…