0
$\begingroup$

Question:

Determine the number of subgroups of index $2$ in $D_{2n}$.

Consider $D_{2n}=\langle r,s|r^n=1, s^2=1, sr=r^{-1}s\rangle$.

Take $N=\langle r\rangle$ and consider canonical homomorphism $G$ to $G/N$.

Then $\langle s\rangle$ is isomorphic to $G/N$. Hence $D_n$ is semidirect product of $C_2$ and $C_n$.

So my claim is there is unique subgroups $N$ of index 2.

Thanks

my argument correct? If so how do I prove the claim.

  • 0
    You haven't made an argument. You've said a few things about $D_{2n}$, and then made an unjustified (and false) assertion about the answer to your question.2012-11-01
  • 0
    sorry for that...2012-11-01

2 Answers 2