Multiplicative groups modulo a number N are used extensively throughout Cryptography. I recently
had a homework assignment on multiplicative groups, and
I spent hours trying to find a decent tutorial on how
to generate them. It's actually really easy, this is what they are.

There are two types of multiplicative groups, ones
to P (a prime) or to N (just a number). For example,

Z*p, where p = 11
would be { p ... p-1 }

Z*n, where n = 12, would include all numbers up until
n-1 whose gcd(x, n) = 1, the set would be,
{ 1, 5, 7, 11 }