Cohomology of finitely presented groups

Locally-finitely-valued Cohomology Groups

Finitely Presented Residually Free Groups

We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all n ∈ N, a residually free group is of type FPn if and only if it is of type Fn. New families of subdirect products of free groups are constructed, including the first examples of finitely presented subgroups ...

Constructing Matrix Representations of Finitely Presented Groups

The Todd-Coxeter coset enumeration algorithm is one of the most powerful tools of computational group theory. It may be viewed as a means of constructing permutation representations of nitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix representations over many elds. In fact the algorithm is more general than this, and can be used to constr...

Decompositions of finitely generated and finitely presented groups

In this paper we discuss the splitting or decomposing of finitely generated groups into free products, free products with amalgamation or HNN extensions and we discuss the JSJ decomposition of finitely presented groups.

Filling radii of finitely presented groups

The filling radius function R of Gromov measures the minimal radii of van Kampen diagrams filling edge-circuits w in the Cayley 2complex of a finite presentation P. It is known that the Dehn function can be bounded above by a double exponential in R and the length of the loop, and it is an open question whether a single exponential bound suffices. We define the upper filling radius R(w) of w to...