Sharp types revisited. (Q1415014)
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scientific article; zbMATH DE number 2012087
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sharp types revisited. |
scientific article; zbMATH DE number 2012087 |
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Sharp types revisited. (English)
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3 December 2003
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The main result of the paper states that for any almost completely decomposable (= acd) (Abelian) group \(X\) (i.e. a torsion-free extension of a completely decomposable group of finite rank by a finite group) its subgroup \(X^\#(\sigma)\) (i.e. the purification of the subgroup of elements of type strictly greater than \(\sigma\)) is a direct summand for any sharp type \(\sigma\) and the complementary summand is acd. This implies that an acd group with some special critical typeset is a direct sum of groups with ranks 1 and 2.
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almost decomposable groups
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purifications
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critical typesets
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direct sums
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