Finite 2-groups with automorphisms of order 4 (Q2746927)
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scientific article; zbMATH DE number 1656865
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite 2-groups with automorphisms of order 4 |
scientific article; zbMATH DE number 1656865 |
Statements
11 October 2001
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residually finite groups
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residually nilpotent groups
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automorphisms
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normal subgroups
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subgroups of finite index
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Finite 2-groups with automorphisms of order 4 (English)
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The following theorem is proven in the article under review: Theorem. If a residually finite or residually nilpotent 2-group \(G\) has an automorphism \(\varphi\) of order 4 such that \(|C_G(\varphi)|=m\) is finite, then \(G\) has a normal subgroup \(H\) of \(m\)-bounded index such that \(H''\leq Z(H)\).
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