On inert subgroups of a group. (Q833480)
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scientific article; zbMATH DE number 5595160
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On inert subgroups of a group. |
scientific article; zbMATH DE number 5595160 |
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On inert subgroups of a group. (English)
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13 August 2009
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Summary: A subgroup \(H\) of a group \(G\) is called inert if \(|H:H\cap H^g|\) is finite for all \(g\) in \(G\). If every subgroup of \(G\) is inert, then \(G\) is said to be inertial. After giving an account of the basic properties of inert subgroups, we study the structure of inertial soluble groups. A classification is obtained for the groups which are finitely generated or have finite Abelian total rank.
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subgroups of finite index
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inert subgroups
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soluble groups
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finitely-generated groups
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groups with finite Abelian total rank
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