Good series! Getting into some new territory for me with homomorphisms and isomorphisms (although I was familiar with the general notion of isomorphic).
What was fun about the subgroups of Z_12 was the connection to the factors of twelve: 2, 3, 4, and 6. I banged out a simple Python app to generate the subgroups for any Z. The subgroups with sizes smaller than Z are always from factors of Z. I hadn't ever realized that connection. Cool!
Good series! Getting into some new territory for me with homomorphisms and isomorphisms (although I was familiar with the general notion of isomorphic).
What was fun about the subgroups of Z_12 was the connection to the factors of twelve: 2, 3, 4, and 6. I banged out a simple Python app to generate the subgroups for any Z. The subgroups with sizes smaller than Z are always from factors of Z. I hadn't ever realized that connection. Cool!