Prove that if H ∪ K is a subgroup of G...
14301
Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
37971
Prove that the center of a group is a normal subgroup
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
129452
Groups $G,H$ with surjective homomorphisms that are quotient of each other
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
149578
Subgroups of $(\mathbb Z_n,+)$
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
102979
If $[G:H]$ and $[G:K]$ are relatively prime, then $G=HK$
151130
When is the product of $n$ subgroups a subgroup?
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
124709
Suppose G be a non-abelian group and H,K be two abelian subgroups of G. Then must HK be an abelian subgroup of G?
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
142228
Proof that a subset closed under group operation of a finite group is a subgroup