Noncancellation and the number of generators

Abstract

We give an example of two groups G and H, generated by 2 and 3 elements, which satisfy G × Z ≅ H × Z.The groups G, H are semi-direct products of a torsion-free abelian group of rank 3 by an infinite cyclic group.

Keywords:

• Non cancellation
• generators
• semidirect product

A.M.S classification number:

• 20E22 (20F16)