Almost fixed-point-free automorphisms of prime power order (Q2818388)
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scientific article; zbMATH DE number 6624867
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Almost fixed-point-free automorphisms of prime power order |
scientific article; zbMATH DE number 6624867 |
Statements
7 September 2016
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soluble group
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Hirsch number
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finite rank group
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fixed points of automorphisms of prime power order
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Almost fixed-point-free automorphisms of prime power order (English)
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Let \(G\) be a group with finite Hirsch number satisfying min-\(q\) for every prime \(q\) and let \(\varphi\) be an automorphism of order \(p^{m}\) of \(G\) such that \(| C_{G}(\varphi) | =p^{c}\) (\(p\) a prime). In this paper, it is proved that \(G\) has a soluble group of derived length bounded only by \(p\), \(m\) and \(c\).NEWLINENEWLINEIn an interesting final remark, the author proves that if \(p^{m}=4\), then \(G\) is a finite extension of a soluble group of derived length at most \(7\).
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