Finitely presented subgroups of automatic groups and their isoperimetric functions

Abstract

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even asynchronously automatic. We can also arrange that such subgroups satisfy, at best, an exponential isoperimetric inequality.

DVI and Post-Script files only. To appear in J. London Math. Soc