# Homomorphic images of Z15.

• May 10th 2009, 12:02 PM
o&apartyrock
Homomorphic images of Z15.
What are all the homomorphic images of Z15 (up to isomorphism)?
• May 10th 2009, 12:16 PM
NonCommAlg
Quote:

Originally Posted by o&apartyrock

What are all the homomorphic images of Z15 (up to isomorphism)?

a homomorphic image of a group G is a group in the form G/K, where K is a normal subgroup of G. in your case $G=\mathbb{Z}/15 \mathbb{Z}$ is abelian. so K is any subgroup of G. find the subgroups of G and then

see what G/K are! the final answer is:

Spoiler:

$(0), \ G, \ \mathbb{Z}/3 \mathbb{Z}, \ \mathbb{Z}/5 \mathbb{Z}.$