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

## Speaker's Institution

Univ. Minho

## Files

José Carlos Costa-19Feb2021.pdf411.33 KB

## Area

Semigroups, Automata and Languages