相关论文: The conjugacy problem for UPG elements of $Out(F_n…

We study in detail the profinite group G arising as geometric \'etale iterated monodromy group of an arbitrary quadratic polynomial over a field of characteristic different from two. This is a self-similar closed subgroup of the group of…

We study the mod-p cohomology of the group Out(F_n) of outer automorphisms of the free group F_n in the case n=2(p-1) which is the smallest n for which the p-rank of this group is 2. For p=3 we give a complete computation, at least above…

We show that all finitely generated free-by-cyclic groups are conjugacy separable: if a finitely generated group $G$ surjects onto $\mathbb{Z}$ with free kernel, then for every pair of non-conjugate elements $g,h\in G$, there exists a…

The Tits alternative for Out(F_n) is reduced to the case where all elements in the subgroup under consideration grow polynomially.

Let $F_n$ be a free group of rank $n$. In this paper we discuss three algorithmic problems related to automorphisms of $F_2$. A word $u$ of $F_n$ is called positive if $u$ does not have negative exponents. A word $u$ in $F_n$ is called…

Let $N \geq 2$ and let $\mathrm{Out}(F_N)$ be the outer automorphism group of a nonabelian free group of rank $N$. Let $\mathrm{IA}_N(\mathbb{Z}/3\mathbb{Z})$ be the finite index subgroup of $\mathrm{Out}(F_N)$ which is the kernel of the…

Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…

A classical conjecture by Graham Higman states that the number of conjugacy classes of $U_n(q)$, the group of upper triangular $n\times n$ matrices over $\mathbb{F}_q$, is polynomial in $q$, for all $n$. In this paper we present both…

Let G be a word-hyperbolic group with given finite generating set, for which various standard structures and constants have been pre-computed. A (non-practical) algorithm is described that, given as input two lists A and B, each composed of…

In this paper we study the conjugacy problem in polycyclic groups. Our main result is that we construct polycyclic groups $G_n$ whose conjugacy problem is at least as hard as the subset sum problem with $n$ indeterminates. As such, the…

We generalize the combinatorial approaches of Rapaport and Higgins--Lyndon to the Whitehead algorithm. We show that for every automorphism $\varphi$ of a free group $F$ and every word $u\in F$ there exists a finite multiset of words…

We give an algorithm to solve the Conjugacy Problem for ascending HNN-extensions of free groups. To do this, we give algorithms to solve certain problems on dynamics of free group endomorphisms.

In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure…

We show that every non-decreasing function $f\colon \mathbb N\to \mathbb N$ bounded from above by $a^n$ for some $a\ge 1$ can be realized (up to a natural equivalence) as the conjugacy growth function of a finitely generated group. We also…

We present a new algorithm that, given two matrices in $GL(n,Q)$, decides if they are conjugate in $GL(n,Z)$ and, if so, determines a conjugating matrix. We also give an algorithm to construct a generating set for the centraliser in…

An algorithm is proposed that solves two decision problems for pseudo-Anosov elements in the mapping class group of a surface with at least one marked fixed point. The first problem is the root problem: decide if the element is a power and…

Let F_n be the free group of rank n, with generating set S=\{x_1,...,x_n\}. An automorphism \phi of F_n is called symmetric if for each 1\leq i\leq n, \phi(x_i) is conjugate to x_j or x_j^{-1} for some 1\leq j\leq n. Let \Sigma Aut(F_n) be…

We study groups $G$ where the $\varphi$-conjugacy class $[e]_{\varphi}=\{g^{-1}\varphi(g)~|~g\in G\}$ of the unit element is a subgroup of $G$ for every automorphism $\varphi$ of $G$. If $G$ has $n$ generators, then we prove that the $k$-th…

A group G is a vGBS group if it admits a decomposition as a finite graph of groups with all edge and vertex groups finitely generated and free abelian. We prove that the multiple conjugacy problem is solvable between two n-tuples A and B of…

We give a short proof of a theorem of Handel and Mosher stating that any finitely generated subgroup of $\text{Out}(F_N)$ either contains a fully irreducible automorphism, or virtually fixes the conjugacy class of a proper free factor of…