### Bounding the orders of finite subgroups

### I. J. Leary and Brita E. A. Nucinkis

Suppose that *G* is a group of rational cohomological dimension
*n* and that *G* is of type FP(*n*) over the
integers. Under these hypotheses we show that there is a bound on the
orders of finite subgroups of *G*. This extends a result of
P. H. Kropholler, who obtained the same conclusion for *G* of
finite rational cohomological dimension and of type FP(infinity) over
the integers.

For each *n*, there are groups *G* of type FP(*n-1*)
over the integers and of rational cohomological dimension *n*
for which there is no bound on the orders of finite subgroups.

Pub. Matematiques 45 (2001) 259-264.