Talk:Cyclic group

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.

In general, some aspects of the article would benefit from a makeover... 2A02:587:4526:EA00:4940:D912:B4:B87C (talk) 00:36, 17 August 2017 (UTC)

Why doesn't it add up? Recall that n there is, as you quote it, the order of the group, not its modulus (necessarily).

~2025-43785-53 (talk) 07:06, 30 December 2025 (UTC)

For a cyclic group, are these not the same? —Antonissimo (talk) 07:05, 31 December 2025 (UTC)

I suspect that your confusion over ${\displaystyle e^{n}}$ is because this article uses a group notation based on multiplication rather than addition. For a group notation using addition, it would instead be ${\displaystyle e\cdot n}$ which, for addition modulo ${\displaystyle n}$, is obviously 0. —David Eppstein (talk) 07:12, 31 December 2025 (UTC)