Title: Exponents and the Cohomology of Finite Groups.
Author: Jonathan Pakianathan
AMS Classification: Primary 20J06, 17B50, 17B56
Address of Author: Department of Mathematics, University of Wisconsin, 
Madison, WI 53706.
Status: Reprint. To appear in "The Proceedings of the A.M.S.".

This paper provides an example of a p-group G which has elements of order p^3
in some of its integral cohomology groups but which also has the property
that p^2 annihilates H^i(G;Z) for all sufficiently high i. This provides
a counterexample to a conjecture of A. Adem which stated that if a finite
group K has an element of order p^n in one of its integral cohomology
groups then it has such an element in infinitely many of its cohomology groups.