Finitistic orders for elements of a free group

A positive integer $n$ is said to be a finitistic order for an element $u$ of a group $F$ if there exist a finite group $G$ and a homomorphism $h$ from $F$ into $G$ such that $h(u)$ has order $n$ (in $G$). Let $u$ be a non-identity element of a free group $F$. It is well known that $u$ has infinite order.  We prove that any positive integer is a finitistic order for $u$.

This is a joint work with Conceição Nogueira and M. Lurdes Teixeira.

Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

Speaker

José Carlos Costa

Univ. Minho

Area

Semigroups, Automata and Languages