query: How to show $\langle x,y \mid x^3=y^3=(xy)^3=1\rangle$ is presentation of an infinite group?
positive_passages.docid: 29445
positive_passages.text: Trying to prove that $H=\langle a,b:a^{3}=b^{3}=(ab)^{3}=1\rangle$ is a group of infinite order.
negative_passages.docid: 127047
negative_passages.text: How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
negative_passages.docid: 33025
negative_passages.text: What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
negative_passages.docid: 156319
negative_passages.text: Show that a group with $|G| = 33$ contains an element of order $3$
negative_passages.docid: 7418
negative_passages.text: The Center of $\operatorname{GL}(n,k)$
negative_passages.docid: 41483
negative_passages.text: Proof relation between Levi-Civita symbol and Kronecker deltas in Group Theory
negative_passages.docid: 18839
negative_passages.text: Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$
negative_passages.docid: 134687
negative_passages.text: Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
negative_passages.docid: 77763
negative_passages.text: Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
negative_passages.docid: 43645
negative_passages.text: Show that $G/H\cong S_3$
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 13834
negative_passages.text: Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
negative_passages.docid: 67796
negative_passages.text: How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
negative_passages.docid: 117000
negative_passages.text: Group presentation for discrete Heisenberg group
negative_passages.docid: 20467
negative_passages.text: Show that $(y_n)\in l^q$
negative_passages.docid: 130488
negative_passages.text: Prove by induction that $3\mid n^3 - n$
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question