On \(p\)-groups with abelian automorphism group (Q1891516)
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scientific article; zbMATH DE number 763291
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(p\)-groups with abelian automorphism group |
scientific article; zbMATH DE number 763291 |
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On \(p\)-groups with abelian automorphism group (English)
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16 January 1996
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In 1913 Miller has shown that there exists a group of order \(2^6\) whose automorphism group is abelian. Here it is shown, that for an odd prime \(p\) no finite non-cyclic \(p\)-group of order \(p^6\) with abelian automorphism group exists. On the other hand, an example of a finite \(p\)- group of order \(p^7\) is given whose automorphism group is abelian. This group is special, is generated by 4 elements, and is the smallest of an infinite family of groups of order \(p^{n^2+3n+3}\), where \(n\) is a natural number.
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Abelian automorphism groups
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finite \(p\)-groups
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