This is a discussion of the relationship between groups using Modular Multiplication and Modular Addition.
Prime Powers are cyclic: https://pi.math.cornell.edu/~mathclub/Media/mult-grp-cyclic-az.pdf
Powers of 2 as a modulus: https://math.stackexchange.com/questions/2460124/multiplicative-group-modulo-2n
Reference: Contemporary Abstract Algebra - Gallian