# What is a simply presented group?

I have some background in commutative ring theory. At the moment I am going through factorization theory of integral domains.

I found out that it is a conjecture, that every Abelian group is the class group of a half-factorial Dedekind domain. I also read, that this was shown for Warfield groups, which are (after Wikipedia) summands of simply presented Abelian groups.

I could not find the definition of a simply presented Abelian group. Has it to do with a presentation of a group by some generating system wrt. some relations? Or is it more like being a finitely presented $$\mathbb{Z}$$-module?

Can somebody give a definition?

• As I understand it, a group is said to be simply presented if it has a presentation where each relation involves at most two generators. – Andreas Caranti Apr 6 at 13:44