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

. Further, we use a fiber product construction to exhibit a family of finitely presented groups

Γ k $\Gamma _k$ normal upper Gamma Subscript k

, where for each k , the conjugator length function of

Γ k $\Gamma _k$ normal upper Gamma Subscript k

grows like functions lying in the k -th level of the Grzegorczyk hierarchy of primitive recursive functions.