This book is about the computational aspects of invariant theory. Of central interest is the
question how the invariant ring of a given group action can be calculated. Algorithms for this …

Questions about modular representation theory of finite groups can often be reduced to
elementary abelian subgroups. This is the first book to offer a detailed study of the …

We classify the 2F-modules for nearly simple groups, excluding the case of modules for
groups of Lie type in their defining characteristic. We also show that for all such modules …

Let F be any field of characteristic p. It is well-known that there are exactly p inequivalent
indecomposable representations V1,..., Vp of Cp defined over F. Thus if V is any …

We describe a new algorithm for decomposing tensor products of indecomposable KG-
modules into a direct sum of indecomposable KG-modules when K is a field of finite …

The Noether number of a representation is the largest degree of an element in a minimal
homogeneous generating set for the corresponding ring of invariants. We compute the …

Consider a group acting on a polynomial ring over a finite field. We study the polynomial ring
as a module for the group and prove a structure theorem with several striking corollaries. For …

Let G be a finite group acting linearly on a vector space V over a field K of positive
characteristic p and let P≤ G be a Sylow p-subgroup. Ellingsrud and Skjelbred [Compositio …

Let V be a finite dimensional representation of ap-group, G, over a field, k, of characteristic p.
We show that there exists a choice of basis and monomial order for which the ring of …

Like the Arabian phoenix rising out of the ashes, the theory of invariants, pronounced dead
at the turn of the century, is once again at the forefront of mathematics. During its long …