Abelianization of a group given by a presentation Suppose $G = \langle x,y\mid x^3 = y^5\rangle$. How can I compute the abelianization of such a group?
Thanks!

When you add the relation $xy = yx$ then all elements can be written in the form $x^ay^b$ with $a, b \in \mathbb{Z}$. Moreover $x^ay^b = e$ precisely when $(a, b)$ is a multiple of $(3, -5)$.  This means that your group is isomorphic to $\mathbb{Z}^2 / \mathbb{Z}(3, -5) \cong \mathbb{Z}$.  (The "precisely" might need some explaining.)
