Advanced mathematicians have difficulty understanding sometimes how the notions they use may be perplexing for everyone non-familiar with their subject. I made some small additions at "Integer and modular addition" and "Modular multiplication" to help explain the notion of "generators" and why, for instance, g must be a coprime to n to be a generator. Feel free to improve if you think you can.
On a general note, however, this article needs a lot of work to become comprehensible for everyone non-expert. The subchapter "Additional properties" seem very hard to grasp for instance, and some things, like "For a finite cyclic group of order n, and every element e of the group, en is the identity element of the group" don't seem to add up, at least as modular arithmetic is concerned.