If $G=G_1\times G_2$ does it follow that $H\leq G \implies H=H_1\times H_2$ where $H_1\leq G_1$ and $H_2\leq G_2$
34567
If $G_1$ and $G_2$ are finite group and $H\leq G_1\times G_2$ then $H=P_1\times P_2$ with $P_i\leq G_i$?
146760
Prove that H is a subgroup of G
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
90845
Is this posible in GR $g_{ab}g^{ab}=1$?
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
105951
Does $G\times K\cong H\times K$ imply $G\cong H$?
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
43645
Show that $G/H\cong S_3$
144732
If $[G:H]=n$, then $g^{n!}\in H$ for all $g\in G$.
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
99630
For every $g\in G$ there exists an $h\in G$ such that $g = h^3$
157840
Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
63162
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
127996
$M_1$ and $M_2$ are subgroups and $M_1/N=M_2/N$. Is $M_1\cong M_2$?
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?