ﻻ يوجد ملخص باللغة العربية
Given a group $G$ and a subset $X subset G$, an element $g in G$ is called quasi-positive if it is equal to a product of conjugates of elements in the semigroup generated by $X$. This notion is important in the context of braid groups, where it has been shown that the closure of quasi-positive braids coincides with the geometrically defined class of $mathbb{C}$-transverse links. We describe an algorithm that recognizes whether or not an element of a free group is quasi-positive with respect to a basis. Spherical cancellation diagrams over free groups are used to establish the validity of the algorithm and to determine the worst-case runtime.
The twin group $T_n$ is a right angled Coxeter group generated by $n-1$ involutions and the pure twin group $PT_n$ is the kernel of the natural surjection from $T_n$ onto the symmetric group on $n$ symbols. In this paper, we investigate some structur
In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include groups of s
We say that a group has property $R_{infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Felshtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{infty}$. We define a solvable
We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups (i.e. fundam
We combine classical methods of combinatorial group theory with the theory of small cancellations over relatively hyperbolic groups to construct finitely generated torsion-free groups that have only finitely many classes of conjugate elements. Moreov