query: Give an example of an infinite group generated by two elements of finite order
positive_passages.docid: 58688
positive_passages.text: Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 59902
negative_passages.text: Example of $2$ non-isomorphic groups that have the same quotients
negative_passages.docid: 148904
negative_passages.text: Groups of order $p^3$
negative_passages.docid: 124224
negative_passages.text: How many groups of order $n$ with center {e} exist?
negative_passages.docid: 42582
negative_passages.text: Infinite group with only two conjugacy classes
negative_passages.docid: 28676
negative_passages.text: Is a finite group uniquely determined by the orders of its elements?
negative_passages.docid: 92750
negative_passages.text: Groups where all elements are order 3
negative_passages.docid: 121423
negative_passages.text: Prove that every element of a finite group has an order
negative_passages.docid: 33593
negative_passages.text: An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
negative_passages.docid: 116080
negative_passages.text: Let G be a finite group with more than one element. Show that G has an element of prime order
negative_passages.docid: 158282
negative_passages.text: Finite order of an element $f(g)$ of a homomorphism $f$
negative_passages.docid: 157841
negative_passages.text: Existence of a non-abelian group of order $p^n$.
negative_passages.docid: 6115
negative_passages.text: Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
negative_passages.docid: 47539
negative_passages.text: Find an abelian infinite group such that every proper subgroup is finite
negative_passages.docid: 5089
negative_passages.text: An element of a group has the same order as its inverse
negative_passages.docid: 58076
negative_passages.text: Subgroup generated by a set