When Any Group of N Elements is Cyclic?

Details When Any Group of N Elements is Cyclic? When Any Group of N Elements is Cyclic?

2011-08-27

arxiv.org/abs/1108.5406v2

Mathematics

Group Theory

4+6 pages, 4 figures, in English and in Russian

Scientific paper

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.

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