Influencer-Generated Reference Groups

Strongly torsion generated groups

It has long been known that the integral homology of a non-trivial finite group must be non-zero in infinitely many dimensions [15]. Recent work on the Sullivan Conjecture in homotopy theory has made it possible to extend this result to non-acyclic locally finite groups. For more general groups with torsion it becomes more difficult to make such a strong statement. Nevertheless we show that whe...

Infinitely Generated Veech Groups

We give a positive response to a question of W. Veech: Infinitely generated Veech groups do exist.

Finitely Generated Abelian Groups

Finitely Generated Semiautomatic Groups

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.

Homogeneously Generated Groups

We develop basic properties of groups that contain exactly k elements of order n and are generated by these elements (called (k, n)-homogeneous groups). We then give a complete classification of (n, n)-homogeneous groups.