 
Summary: Z .JOURNAL OF ALGEBRA 182, 721 737 1996
ARTICLE NO. 0197
Automorphisms and Cohomology of Discrete Groups
Alejandro AdemU
Department of Mathematics, Unišersity of Wisconsin, Madison, Wisconsin 53706
Communicated by Richard G. Swan
Received March 27, 1995
INTRODUCTION
Let denote a discrete group of finite cohomological dimension.
Calculating the cohomology of such groups is notoriously difficult, involv
ing complicated geometric information attached to the group. For exam
ple, the cohomology of torsionfree arithmetic groups involves delicate
questions about symmetric spaces and number theory. Perhaps the key
difficulty lies in that there is no practical method for building up the
Zcohomology of from that of its subgroups such as one can do for finite
.groups .
In this paper we outline a method for constructing nontrivial classes in
U
Z . Z .H , where denotes a field with p elements based on the use ofp p
finite automorphism groups of . Given an explicit presentation for ,
