Verbal small cancellation

Geometric small cancellation

A General Small Cancellation Theory

In this article a generalized version of small cancellation theory is developed which is applicable to specific types of high-dimensional simplicial complexes. The usual results on small cancellation groups are then shown to hold in this new setting with only slight modifications. For example, arbitrary dimensional versions of the Poincaré construction and the Cayley complex are described.

The Burnside Groups and Small Cancellation Theory

In a pair of recent articles, the author develops a general version of small cancellation theory applicable in higher dimensions ([5]), and then applies this theory to the Burnside groups of sufficiently large exponent ([6]). More specifically, these articles prove that the free Burnside groups of exponent n ≥ 1260 are infinite groups which have a decidable word problem. The structure of the fi...

Nielsen Equivalence in Small Cancellation Groups

Let G be a group given by the presentation 〈a1, . . . , ak , b1, . . . bk | ai = ui(b̄), bi = vi(ā) for 1 ≤ i ≤ k〉, where k ≥ 2 and where the ui ∈ F (b1, . . . , bk) and wi ∈ F (a1, . . . , ak) are random words. Generically such a group is a small cancellation group and it is clear that (a1, . . . , ak) and (b1, . . . , bk) are generating n-tuples for G. We prove for generic choices of u1, . . ....

On a small cancellation theorem of Gromov

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from