$x$ and $y$ be distinct elements of order $2$ in $G$ that generate $G$. Prove that $G \cong D_{2n}$
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
88440
Is G a CLT group if its order is product of distinct prime?
62455
Prove Equivalence Relation in G
78564
Prove: $D_{8n} \not\cong D_{4n} \times Z_2$.
103146
Proof that the Rubik’s Cube group is 2-generated
121707
Generating Elements of Galois Group
77128
Necessary and Sufficient conditions for $(i \, j)$ and $(1 \, 2 \, \dotsc \, n)$ generate $S_n$.
84789
Order of products of elements in a finite Abelian group
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
100605
let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
46687
Elements of $GL_{2}(\mathbb{Z})$ of finite order
148413
Proving $S_n$ is generated by the set $\{(1\text{ }2),(2\text{ }3),\cdots,(n-1\text{ }n)\}$ of $n-1$ transpositions.
94420
Dihedral group - elements of order $2$
89659
$H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
74924
identity element of $(D_n ,\gcd)$
35660
Elements of order 2 in $D_{2n}$