  We define pseudo-Garside groups and prove a theorem about them parallel to
Garside's result on the word problem for the usual braid groups. The main
novelty is that the set of simple elements can be infinite. We introduce a
group B=B(Z^n) which we call the braid group of Z^n, and which bears some vague
resemblance to mapping class groups. It is to GL(n,Z) what the braid group is
to the symmetric group S_n. We prove that B is a pseudo-Garside group. We give
a small presentation for B(Z^n) assuming one for B(Z^3) is given.
