query: Are $g_1$ and $g_2$ elements of $\langle g_1g_2\rangle$ when $g_1$ and $g_2$ commute and have co-prime orders?
positive_passages.docid: 158074
positive_passages.text: Cyclic group $G$ with generator $ab$.
negative_passages.docid: 108325
negative_passages.text: What's the relationship between $SL(2,\mathbb{C})$, $SU(2)\times SU(2)$ and $SO(1,3)$?
negative_passages.docid: 108767
negative_passages.text: Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
negative_passages.docid: 89659
negative_passages.text: $H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
negative_passages.docid: 39096
negative_passages.text: Primitive elements of GF(8)
negative_passages.docid: 37061
negative_passages.text: The order of $ab$ when $a,b$ commute
negative_passages.docid: 45028
negative_passages.text: How to show that $\langle a \rangle$ is a subgroup of a group $G$, where $a$ is in center of the group $G$
negative_passages.docid: 37414
negative_passages.text: Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
negative_passages.docid: 90845
negative_passages.text: Is this posible in GR $g_{ab}g^{ab}=1$?
negative_passages.docid: 125345
negative_passages.text: Suppose $a$ and $b$ are group elements, $a$ and $b$ commute, $|a|$ and $|b|$ are both finite. What are the possibilities for $|ab|$?
negative_passages.docid: 14895
negative_passages.text: Reference for the subgroup structure of $\rm{PSL}_2(q)$
negative_passages.docid: 15630
negative_passages.text: Normal subgroup of prime order is characteristic
negative_passages.docid: 1720
negative_passages.text: Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
negative_passages.docid: 119758
negative_passages.text: On the order of elements of $\mathrm{GL}(2,q)$.
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 127996
negative_passages.text: $M_1$ and $M_2$ are subgroups and $M_1/N=M_2/N$. Is $M_1\cong M_2$?
negative_passages.docid: 91774
negative_passages.text: Existence of group $G$ with $|G|>2$ and automorphism group of odd order