Finitely Generated Abelian Groups and Similarity of Matrices over a Field

At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common.  However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases.  Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only i