Proof that $A_n$ the only subgroup of $ S_n$ index $2$.
1996
$A_n$ is the only subgroup of $S_n$ of index $2$.
98474
Show the existence of a certain subgroup of F2
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
108310
$(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group
142228
Proof that a subset closed under group operation of a finite group is a subgroup
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
131594
Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
156154
Sylow 2 subgroups of S4
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
146760
Prove that H is a subgroup of G
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
142938
Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$
129485
A subgroup of a cyclic group is cyclic - Understanding Proof
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
19352
Normal subgroup of index m contains every element of order n where m and n are relatively prime