The purpose of this book is to study the relation between the
representation ring of a finite group and its integral cohomology by
means of characteristic classes. In this way it is possible to extend
the known calculations and prove some general results for the integral
cohomology ring of a group G of prime power order. Among the groups
considered are those of p-rank less than 3, extra-special p-groups,
symmetric groups and linear groups over finite fields. An important tool
is the Riemann - Roch formula which provides a relation between the
characteristic classes of an induced representation, the classes of the
underlying representation and those of the permutation representation of
the infinite symmetric group. Dr Thomas also discusses the implications
of his work for some arithmetic groups which will interest algebraic
number theorists. Dr Thomas assumes the reader has taken basic courses
in algebraic topology, group theory and homological algebra, but has
included an appendix in which he gives a purely topological proof of the
Riemann - Roch formula.