We apply the equivariant Burnside group formalism to distinguish linear actions of finite groups, up birationality. Our approach is based on De Concini–Procesi models subspace arrangements.

If G is a word hyperbolic group of cohomological dimension 2, then every subgroup of G of type FP2 is also word hyperbolic. Isoperimetric inequalities are denned for groups of type FP2 and it is shown that the linear isoperimetric inequality in this generalized context is equivalent to word hyperbolicity. A sufficient condition for hyperbolicity of a general graph is given along with an applica...

Let p be a prime number. This paper describes the primitive idempotents and prime spectrum of the crossed Burnside algebra of a finite group over a p-local ring. The main application is a formula for the block idempotents of the p-local Mackey algebra of the group, in terms of the corresponding blocks of the group algebra. Mathematics Subject Classification (2000): 19A22 20C20

In a 1969 article, A. Dress described the prime ideals of Burnside ring finite group G and inclusion relations between them. One may ask whether similar results exist for saturated fusion system F over p-group S. The present paper answers positively, providing typology A(F) those A(F)(p) as consequence.

In this paper we investigate some properties of the Burnside ring a profinite group as defined in [5]. We introduce notion crossed FC-group, and generalise results from finite to (FC-)groups. our investigations, also obtain on FC-groups which may be independent interest.

The problem of finding regularity conditions for languages is, via the syntactic monoid, closely related to the classical Burnside problem. This survey paper presents several results and conjectures in this direction as well as on related subjects, including bounded languages, pumping, square-free words, commutativity, and rational power series.

We define for arbitrary modules over a finite von Neumann algebra A a dimension taking values in [0,∞] which extends the classical notion of von Neumann dimension for finitely generated projective A-modules and inherits all its useful properties such as Additivity, Cofinality and Continuity. This allows to define L2-Betti numbers for arbitrary topological spaces with an action of a discrete gro...