Prove that $S^k$ is a subgroup of $G$
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
28181
Sylow subgroups of $S_3$ and $S_4$
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
117468
$o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
104855
Prove that $N \subset Z(G)$
110217
$GL(n,K)$ is open in $M(n,K)$
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
99999
A question on identifying normal subgroups of $S_4$
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
65744
How can I Prove that H=G or K=G
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$
130081
Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.