A semigroup with linearithmic Dehn function.

It is known that no finitely presented group has the Dehn function asymptotically strictly between linear and quadratic functions. We present an example of a semigroup whose Dehn function is equivalent to n log n , thus strictly inside the said gap. The example is obtained by symmetrizing the rewriting rules of a particular semi-Thue system, which has the derivational complexity function n log n . [ABSTRACT FROM AUTHOR]