If $H,K$ are subgroups of $G$, then $HK = G$?
6030
Group of order 15 is abelian
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
128834
Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
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?
94469
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
102979
If $[G:H]$ and $[G:K]$ are relatively prime, then $G=HK$
43750
Subgroups of finite solvable groups. Solvable?
2174
Proving that HK is a subgroup when K is normal
28722
Prove that $H$ is a abelian subgroup of odd order
102622
K is a subgroup of G. Show that K is not a normal subgroup
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
85129
If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$