Groups with fast-growing conjugator length functions

Abstract

We construct the first examples of finitely presented groups whose conjugator length function is exponential; these are central extensions of groups of the form $F_m⋊F_2$. Further, we use a fibre product construction to exhibit a family of finitely presented groups ${\Gamma }_k$ where, for each $k$, the conjugator length function of ${\Gamma }_k$ grows like functions lying in the $k$-th level of the Grzegorczyk hierarchy of primitive recursive functions.

23 pages, no figures