When Any Group of N Elements is Cyclic?
Group Theory
2026-01-08 v3 History and Overview
Abstract
We give a simple proof of the well-known fact: any group of n elements is cyclic if and only if n and \phi(n) are coprime. This note is accessible for students familiar with permutations and basic number theory. No knowledge of abstract group theory is required; a few necessary notions are introduced in the course of the proof. The note could also be an interesting easy reading for mature mathematicians.
Cite
@article{arxiv.1108.5406,
title = {When Any Group of N Elements is Cyclic?},
author = {V. Bragin and Ant. Klyachko and A. Skopenkov},
journal= {arXiv preprint arXiv:1108.5406},
year = {2026}
}
Comments
3+13 pages, 4 figures, in English and in Russian, Russian version extended