The commensurability relation for finitely generated groups

The Commensurability Relation for Finitely Generated Groups

There does not exist a Borel way of selecting an isomorphism class within each commensurability class of finitely generated groups.

The bi-embeddability relation for finitely generated groups II

We study the isomorphism and bi-embeddability relations on the spaces of Kazhdan groups and finitely generated simple groups.

The bi-embeddability relation for finitely generated groups

There does not exist a Borel selection of an isomorphism class within each bi-embeddability class of finitely generated groups.

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.