On nilpotent groups having an almost regular automorphism of prime order (Q1920776)
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scientific article; zbMATH DE number 917073
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On nilpotent groups having an almost regular automorphism of prime order |
scientific article; zbMATH DE number 917073 |
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On nilpotent groups having an almost regular automorphism of prime order (English)
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24 November 1996
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We extend the result of an earlier paper [ibid. 33, No. 5, 206-208 (1992; Zbl 0786.20025)] by analogy. Theorem. If a nilpotent group \(G\) admits an automorphism \(\varphi\) of prime order \(p\) with a finite number \(q\) of fixed points, then for some function \(s(p,q)\) the subgroup \(G^{s(p,q)}\) generated by all \(s(p,q)\)th powers is nilpotent of class \(\leq h(p)\).
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automorphisms of prime order
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finite number of fixed points
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nilpotent groups
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subgroups
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