Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups

Isoperimetric Functions of Finitely Generated Nilpotent Groups

We show that the isoperimetric function of a nitely generated nilpotent group of class c is bounded above by a polynomial of degree 2c.

Testing polycyclicity of finitely generated rational matrix groups

We describe algorithms for testing polycyclicity and nilpotency for finitely generated subgroups of GL(d,Q) and thus we show that these properties are decidable. Variations of our algorithm can be used for testing virtual polycyclicity and virtual nilpotency for finitely generated subgroups of GL(d,Q).

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.

Combinatorics of Finitely Generated Groups

of the Dissertation Combinatorics of Finitely Generated Groups