Last problem I can't figure out.

Find all the homomorphic images of the following groups, D4 and Q.

I would really really appreciate any help. Thanks in advance.

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- Dec 2nd 2006, 07:09 PMnanotek887homomorphic images
Last problem I can't figure out.

Find all the homomorphic images of the following groups, D4 and Q.

I would really really appreciate any help. Thanks in advance. - Dec 3rd 2006, 06:37 AMThePerfectHacker
The homomorphic image of $\displaystyle D_4$ must be a subgroup of Q.

Those all the**possible**homomorphic images are subgroups of Q.

Thus,

$\displaystyle \{1\}$

$\displaystyle \{1,-1\}$

$\displaystyle \{1,-1,i,-i\}$

$\displaystyle \{1,-1,j,-j\}$

$\displaystyle \{1,-1,k,-k\}$

$\displaystyle \{1,-1,i,-i,j,-j,k,-k\}$

You can also look heir. - Dec 3rd 2006, 08:49 AMnanotek887
So those are the homomorphic images of D4?

What's Q then? - Dec 3rd 2006, 08:52 AMThePerfectHacker
- Dec 3rd 2006, 09:36 AMnanotek887
But are the homomorphic images of Q the subgroups of anything else like the one before?

- Dec 3rd 2006, 11:12 AMThePerfectHacker
Similarly the homomorphic images of Q are the subgroups of D4