When is \(Z_ n\) the only group of order \(n\)? (Q1314957)
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scientific article; zbMATH DE number 509051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | When is \(Z_ n\) the only group of order \(n\)? |
scientific article; zbMATH DE number 509051 |
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When is \(Z_ n\) the only group of order \(n\)? (English)
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15 January 1996
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The authors present yet another proof of the well-known fact that \(\mathbb{Z}_n\) is the unique group of order \(n\) iff \((n, \varphi(n)) = 1\), \(\varphi\) Euler's function. A similar, and even more detailed, proof was recently published by \textit{D. Jungnickel} [in Am. Math. Mon. 99, No. 6, 545-547 (1992; Zbl 0779.20011)].
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uniqueness of cyclic groups
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group of order \(n\)
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