When Any Group of N Elements is Cyclic?
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2011
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| Subjects: | |
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| _version_ | 1866908750291402752 |
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| author | Bragin, V. Klyachko, Ant. Skopenkov, A. |
| author_facet | Bragin, V. Klyachko, Ant. Skopenkov, A. |
| contents | We give a simple proof of the well-known fact: any group of n elements is cyclic if and only if n and ϕ(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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1108_5406 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | When Any Group of N Elements is Cyclic? Bragin, V. Klyachko, Ant. Skopenkov, A. Group Theory History and Overview 20E99 We give a simple proof of the well-known fact: any group of n elements is cyclic if and only if n and ϕ(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. |
| title | When Any Group of N Elements is Cyclic? |
| topic | Group Theory History and Overview 20E99 |
| url | https://arxiv.org/abs/1108.5406 |