In this article, we prove that any automorphism of R. Thompson`s group F has infinitely many twisted conjugacy classes. The result follows from the work of Brin, together with standard facts about R. Thompson`s group F, ...

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies ...

We determine twisted conjugacy classes of type D associated with the sporadic simple groups. This is an important step in the program of the classification of finite-dimensional pointed Hopf algebras with non-abelian ...

In this paper, we study the Reidemeister spectrum for metabelian groups of the form Q(n) x Z and Z[1/p](n) x Z. Particular attention is given to the R(infinity)-property of a subfamily of these groups.

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated ...

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely ...

This essay is a detailed introductory study of Combinatorial Group Theory and one of its three classical problems: the Conjugacy Problem. We studied its solution for several classes of group extensions, obtained in [1] and ...

Sea C una categoría de fusión íntegra, en este trabajo se estudian algunos grafos, llamados el grafo primo y el grafo común divisor, relacionados con las dimensiones de Frobenius-Perron de los objetos simples de C. Estos ...

Let (Formula presented.) be an integral fusion category. We study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects in the category (Formula ...