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.
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.