Proving $r^{k}$ is the only nonidentity element of $D_{2n}$ that commutes with all elements for even $n$
11393
The center of the dihedral group
121880
How to show that $|D_{2n}| = 2n$ via the presentation?
104349
Proof by induction involving symmetric groups
156383
Proving a combinatorial identity without double counting
87238
$(1 2)(3 4)$ does not commute with any nonidentity element of odd order in $A_5$.
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
24561
$\mathbb S_n$ as semidirect product
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
45958
Proof that the Euler characteristic is additive
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
103854
Showing that $Q_n=D_n+D_{n-1}$
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
78564
Prove: $D_{8n} \not\cong D_{4n} \times Z_2$.
103106
Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
67926
$S_n$ is generated by elements of the form $(1k)$