Chapter 10
Exercise
1. This software determines the homomorphisms from Zm
to Zn. (Recall that a homomorphism from Zm
is completely determined by the image of 1.)
Run the program
for m
= 20 with various choices for n. Run the program for m = 15
with various choices for n. What relationship do you see between m
and n and the number of homomorphisms from Zm to
Zn? For each choice of m and n, observe
the smallest
positive image of 1. Try to see the relationship between this image and the
values of m and n. What relationship do you see between the
smallest positive image of 1 and the other images of 1? Test your conclusions
with other choices of m and n.