On Brauer’s Height Zero Conjecture
In this paper, the unproven half of Richard Brauer’s Height Zero Conjecture is reduced to a question on simple groups.
On certain homotopy actions of general linear groups on iterated products
The -fold product of an arbitrary space usually supports only the obvious permutation action of the symmetric group . However, if is a -complete, homotopy associative, homotopy commutative -space one can define a homotopy action of on . In various cases, e.g. if multiplication by is null homotopic then we get a homotopy action of for some . After one suspension this allows one to split using idempotents of which can be lifted to . In fact all of this is possible if is an -space...
On characters with minimal defects.
On faithful projective representations of finite abelian p-groups over a field of characteristic p
Let G be a noncyclic abelian p-group and K be an infinite field of finite characteristic p. For every 2-cocycle λ ∈ Z²(G,K*) such that the twisted group algebra is of infinite representation type, we find natural numbers d for which G has infinitely many faithful absolutely indecomposable λ-representations over K of dimension d.
On Groups with Several Doubly-Transitive Permuation Representations.
On indecomposable projective representations of finite groups over fields of characteristic p > 0
Let G be a finite group, F a field of characteristic p with p||G|, and the twisted group algebra of the group G and the field F with a 2-cocycle λ ∈ Z²(G,F*). We give necessary and sufficient conditions for to be of finite representation type. We also introduce the concept of projective F-representation type for the group G (finite, infinite, mixed) and we exhibit finite groups of each type.
On Lie powers of regular modules in characteristic 2
On modular projective representations of finite nilpotent groups
Our aim is to determine necessary and sufficient conditions for a finite nilpotent group to have a faithful irreducible projective representation over a field of characteristic p ≥ 0.
On monomial groups.
On perfect isometries and isotypies in finite groups.
On the cohomology of groups of p-length 1.
On the decomposition map of Grothendieck groups.
On the decomposition numbers of the finite unitary groups in non-defining characteristic.
On the Loewy-series of the modular group algebra of a finite p-group.
On the Modular Representations of the General Linear and Symmetric Groups.
On the monomiality of groups of order between 100 and 200. I.
On the Number of Characters in Blocks of Finite General Linear, Unitary and Symmetric Groups.
On the Schur Indices of Characters of GL (2, q) and GL (3, q).
On the structure of induced modules and tensor induction for group representations
On the vertices of modules in the Auslander-Reiten quiver.