What is the name of a free abelian group $G$ with the relation $\sum b_i = 0$, where $b_i$ is the basis of $G$? And is there any good introductory literature on these objects?

  • $\begingroup$ Why do you think there is a standard name? It's just the free abelian group of rank $n-1$. $\endgroup$ – lhf Aug 31 '17 at 1:33
  • $\begingroup$ I think that answers the question then. I'm not a group theorist, but I've started studying objects that have this group structure and didn't know how to find out more about it. $\endgroup$ – Salt Aug 31 '17 at 1:37
  • $\begingroup$ Don't the $b_i$ need to be linearly independent to form a basis? $\endgroup$ – Fly by Night Aug 31 '17 at 1:38

If $G$ is a free abelian group of rank $n$ with basis $b_1,\dots,b_n$, then $G$ mod the relation $\sum b_i = 0$ is a free abelian group of rank $n-1$.


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