 Abelian group presentation

An abelian group presentation specifies generators of a group and additive relations. For generators $e_1,\dots ,e_n$, let $L$ be the subgroup of ${\mathbb{Z}}^n$ generated by the relation vectors; the presented abelian group is ${\mathbb{Z}}^n/L$. The orders of the images of the generators can be smaller than the orders imposed by individual relations. A relation $d{e}_i=0$ only requires that the order of a group element divide $d$.