Providing a nearly complete selection of up-to-date methods and results on block invariants
with respect to their defect groups this book covers the classical theory pioneered by Brauer
the modern theory of fusion systems introduced by Puig the geometry of numbers developed by
Minkowski the classification of finite simple groups and various computer assisted methods.
In a powerful combination these tools are applied to solve many special cases of famous open
conjectures in the representation theory of finite groups. Most of the material is drawn from
peer-reviewed journal articles but there are also new previously unpublished results. In order
to make the text self-contained detailed proofs are given whenever possible. Several tables
add to the text's usefulness as a reference. The book is aimed at experts in group theory or
representation theory who may wish to make use of the presented ideas in their research.
