A sub-theorem inside "Prove that The group $A_4$ has no subgroup of order $6$".
76943
Existence of subgroup of order six in $A_4$
18198
Lang Algebra Chapter 6 Theorem 9.4
132856
Find the derived subgroup of $A_4$
1996
$A_n$ is the only subgroup of $S_n$ of index $2$.
8746
Groups of order $pq$ without using Sylow theorems
98542
Prove that $H$ is a subgroup of an abelian group $G$
151130
When is the product of $n$ subgroups a subgroup?
91021
Torsion elements of a group aren't necessarily a subgroup
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
139451
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
93666
Does the closedness of a subgroup $H$ of $G$ imply that for $h\in H, g\in G \setminus H : hg \not \in H$?
74586
Prove that every group of order $4$ is abelian
99309
Groups of order $n^2$ that have no subgroup of order $n$
53990
Group with more than one element and with no proper, nontrivial sub groups must have prime order.
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
132816
$A_4 \oplus Z_3$ has no subgroup of order 18
134376
Let $G$ be a nonabelian group. Let $a \in G$ have order $4$ and let $b \in G$ have order $3$. Then the order of the element $ab$ in $G$