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Abstract Algebra

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Right Cosets of Dihedral Group

ABSALG-1NRXVL

Let $G=\langle r,s: r^5=s^2=1, srs=r^{-1}\rangle$ be the dihedral group of order 10. Determine the right cosets of the subgroup $H=\{1, r^3s\}$ in $G$.

A

$H$, $\{r,r^4s\}$, $\{r^2, s\}$, $\{r^3,rs\}$, $\{r^4,r^2s\}$

B

$H$, $\{r,r^2s\}$, $\{r^2, rs\}$, $\{r^3,r^4s\}$, $\{r^4,s\}$

C

$H$, $\{r,r^2s\}$, $\{r^2, rs\}$, $\{r^3,s\}$, $\{r^4,r^4s\}$

D

$\{1, s\}$, $\{r,r^4\}$, $\{r^2,r^3s\}$, $\{r^3, rs\}$, $\{r^2s,r^4s\}$