Splittings of infinite Abelian groups (Q1073919)
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scientific article; zbMATH DE number 3946457
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Splittings of infinite Abelian groups |
scientific article; zbMATH DE number 3946457 |
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Splittings of infinite Abelian groups (English)
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1986
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Minkowski's problem concerning tilings of Euclidean space by cubes was solved by \textit{G. Hajós} [see Math. Z. 47, 427-467 (1941; Zbl 0025.25401)]. He reduced Minkowski's geometrical problem to a problem in finite group theory involving a factorization of a finite group. The principal result of the present paper is a prime decomposition theorem for splittings of \(\mathbb{Z}\) (the additive group of integers).
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tilings of Euclidean space
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factorization
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prime decomposition theorem
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splittings of \(\mathbb{Z}\)
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