Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis.
For a G-covering Y → Y/G = X induced by a properly discontinuous action of a group G on a topological space Y, there is a natural action of π(X,x) on the set F of points in Y with nontrivial stabilizers in G. We study the covering of X obtained from the universal covering of X and the left action of π(X,x) on F. We find a formula for the number of fixed points of an element g ∈ G which is a generalization of Macbeath's formula applied to an automorphism of a Riemann surface. We give a new method...
Two mappings from a CW-complex to a 1-dimensional CW-complex are homotopic if and only if their restrictions to finite subcomplexes are homotopic.
We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...
For a finite group denote by the set of conjugacy class sizes of . In 1980s, J. G. Thompson posed the following conjecture: If is a finite nonabelian simple group, is a finite group with trivial center and , then . We prove this conjecture for an infinite class of simple groups. Let be an odd prime. We show that every finite group with the property and is necessarily isomorphic to , where .