On a property of \(\omega\)-stable solvable groups (Q1112809)
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scientific article; zbMATH DE number 4079395
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a property of \(\omega\)-stable solvable groups |
scientific article; zbMATH DE number 4079395 |
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On a property of \(\omega\)-stable solvable groups (English)
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1988
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It is a very famous result that an \(\omega\)-stable group has an infinite abelian subgroup. In the paper, it is shown that if G is a connected solvable group of finite Morley rank, then: (1) G is \(\aleph_ 1\)- categorical, or (2) G has a definable abelian group with Morley rank \(\geq 2\). It is also shown that if G is nilpotent in the above, then (2) can be replaced by (2)' Z(G) has Morley rank \(\geq 2\).
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\(\omega\)-stable group
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abelian subgroup
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solvable group
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finite Morley rank
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