-systems of finite simple groups
Testing Cayley graph densities
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an -generated group is amenable if and only if the density of the corresponding Cayley graph equals to . We test amenable and non-amenable...
The accessibility of finitely presented groups.
The averaged Dehn function relative to a given probability measure.
The Bass conjecture and growth in groups
We discuss Bass's conjecture on the vanishing of the Hattori-Stallings rank from the viewpoint of geometric group theory. It is noted that groups without u-elements satisfy this conjecture. This leads in particular to a simple proof of the conjecture in the case of groups of subexponential growth.
The braid groups of the projective plane.
The classification of groups in which every product of four elements can be reordered
The conjugacy problem for groups, and Higman embeddings.
The conjugacy-vectors of all relative holomorphs of an elementary Abelian group of order 16
The Coxeter group .
The distribution of descents and length in a Coxeter group.
The dual braid monoid
The equation in partially commutative groups.
The equation in partially commutative groups.
The fixed group of an automorphism of a word hyperbolic group is rational.
The genus problem for one-relator products of locally indicable groups.
The geometric invariants of direct products of virtually free groups.
The group Sp10(ℤ) is (2,3)-generated
It is proved that the group Sp10(ℤ) is generated by an involution and an element of order 3.
The Grushko decomposition of a finite graph of finite rank free groups: an algorithm.
The homology of Peiffer products of groups.