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?

  • 2
    $\begingroup$ 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. $\endgroup$ – Andreas Caranti Apr 6 at 13:44
  • $\begingroup$ Many thanks! Can you recommend a book, where one can read more about this? $\endgroup$ – Daniel W. Apr 6 at 14:58

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