Author: Philip Osterlund
Institution: University of Minnesota

Abstract: This thesis is aimed towards the determination of tensor 
decompositions of the regular representation of finite p-groups over 
fields of characteristic p. We also focus on uniserial modules, as they 
are often factors. We develop an algorithm that determines, up to 
isomorphism, all uniserial modules of a group ring (Section 2, pp. 
11-12). In a tensor decomposition of the regular representation of a 
group, we relate the Loewy lengths, radical series and socle series of 
the regular representation to those of the factors (Theorems 1.4-1.7, pp. 
69-74). Under certain conditions, we find that the Poincare polynomial 
associated to the filtration of a module is the product of the 
corresponding Poincare polynomials of the module's tensor factors 
(Corollary 1.8, p.73). For the non-abelian groups of order 16 that can 
not be written as direct products of proper subgroups we classify the 
uniserial modules (Chapter 2, pp. 23-66) and all tensor decompositions 
(Section 3, pp. 85-111).

Status of paper: This is a University of Minnesota thesis which was 
accepted for the degree of Ph.D. in 1997. The subject matter of the 
thesis has not yet appeared elsewhere.