0
$\begingroup$

In the group $\Bbb Z_{24}$, let $H=\langle 4\rangle $ and $N=\langle 6\rangle $

1) List the elements of $HN$. I found $HN=\{0,2,4,\cdots,22\}=\langle 2\rangle$

2) List the elements of $H\cap N$. I found $H\cap N=\{0,12\}=\langle 12\rangle$

3) List the cosets of $HN/N$. How do I do this?

$\endgroup$
2
$\begingroup$

Simply list the cosets. Two cosets $a+N$, $b+N$ will be the same if $a-b$ is divisible by $6$. $$0+N=N$$ $$2+N=\{2,8,14,20\}$$ $$4+N=\{4,10,16,22\}$$ We know there are only $3$ since $|HN|/|N|=3$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.