Prove that a symmetric group $S_n$ has a cyclic subgroup of order $n$.
50762
If $S_n$ has cyclic subgroups of these orders or not?
117899
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
30003
Proving that Order for N is Anti-symmetric
104349
Proof by induction involving symmetric groups
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
121423
Prove that every element of a finite group has an order
150156
Proving that $S_n$ has order $n!$
158074
Cyclic group $G$ with generator $ab$.
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
61513
Prove that all cyclic groups of the same order are isomorphic
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
128834
Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
137691
What are the self-normalizing subgroups of $S_n$?
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$