# Right coset of a subgroup H in G

Let $H = \left \{(1),(12)(34),(13)(24),(14)(23)\right \}$ be a subset of $G = S_4$. Observe that $H$ is a subgroup of $G$. Determine the set of right cosets of $H$ in $G$. Let $K=G_1$ and show that the elements of $K$ give a distinct set of coset representatives for $H$ in $G$.

Definition: The right coset of the subgroup H in a group G containing the element g is the set $Hg=\left \{ hg|h \in H \right \}$

Is there another way to interpret "Let $K =G_1$ and show that the elements of $K$ give a distinct set of coset representatives for $H$ in $G$."? The examples I have looked at were all pretty straight forward. I'm sure I do not understand this question.

• Excuse me, what is $G_1$? – marco trevi Mar 31 '16 at 11:43