Question on Group Presentation

Is it true that $\mathbb{Z}^{2}*\mathbb{Z}^{2}$ has a group presentation: $\langle a,b,c,d|ab=ba,cd=dc\rangle$. If not, what is the correct group presentation. Thanks!

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Yes, it is true. – Andrea May 19 '12 at 15:07
@Andrea: maybe you should post that as an answer? (perhaps with some notes why) – Ben Millwood May 19 '12 at 17:54

Let $\,\{a,b\}\,\,,\,\,\{c,d\}\,$ be the (free abelian) generators of the first and second factors, resp., in the free product. Clearly, $\,ab=ba\,\,,\,\,cd=dc\,$ are relations in each of these factors resp. and, thus, also in the free product, and there can't be any more relations as both factors are free abelian groups in those generators.