2-Potenzen der Ordnung von Einheitengruppen unimodularer definiter \({\mathbb{Z}}\)-Gitter. (Two-part of the order of unit groups of unimodular definite \({\mathbb{Z}}\)-lattices) (Q919382)
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scientific article; zbMATH DE number 4160836
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 2-Potenzen der Ordnung von Einheitengruppen unimodularer definiter \({\mathbb{Z}}\)-Gitter. (Two-part of the order of unit groups of unimodular definite \({\mathbb{Z}}\)-lattices) |
scientific article; zbMATH DE number 4160836 |
Statements
2-Potenzen der Ordnung von Einheitengruppen unimodularer definiter \({\mathbb{Z}}\)-Gitter. (Two-part of the order of unit groups of unimodular definite \({\mathbb{Z}}\)-lattices) (English)
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1990
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Let L be a unimodular positive definite n-dimensional \({\mathbb{Z}}\)-lattice with orthogonal group O(L). Let \(I_ n=\perp^{n}_{i=1}<1>\). It is proved that if the two-part of \(| O(L)|\) is greater or equal than the two-part of \(| O(I_ n)|\) then L \(\cong I_ n\). Further a similar theorem for even unimodular positive definite \({\mathbb{Z}}\)-lattices is proved.
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unimodular positive definite n-dimensional \({\mathbb{Z}}\)-lattice
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