On torsion-free barely transitive groups (Q2703120)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On torsion-free barely transitive groups |
scientific article |
Statements
7 February 2002
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barely transitive groups
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FC-groups
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periodic groups
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\(p\)-groups
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locally finite groups
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centralizers
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unions of normal subgroups
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On torsion-free barely transitive groups (English)
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A group \(G\) is called barely transitive, if it acts transitively and faithfully on an infinite set and every orbit of every proper subgroup of \(G\) is finite. The author shows that if \(G\) is barely transitive and if the centralizer of a non-trivial element is infinite and contains the stabilizer of a point, then \(G\) is not simple. Moreover, a barely transitive group \(G\) is the union of an increasing sequence of proper normal subgroups if and only if \(G\) is locally finite.
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