Group and subgroup proof
93596
If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
51352
Subgroups of a finite abelian group
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
87766
Using Cayley's Theorem to find an isomorphic subgroup.
14301
Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
92873
To prove in a Group Left identity and left inverse implies right identity and right inverse
79933
Let $G$ be a group and $c\in G$. Define $*$ on $G$ by: $x*y=xdy$ for all $x,y\in G$, where $d$ is the inverse of $c$. Prove $(G,*)$ is a group.
116936
Commutator subgroup and subgroup generated by square.
26624
Prove that is group is abelian
15210
Group of order 6 proof
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
98474
Show the existence of a certain subgroup of F2
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
157330
Showing the image of a subgroup is a subgroup.
132127
Proving a direct product of groups is a group
8742
Examples and further results about the order of the product of two elements in a group