A simple proof of Baer's and Sato's theorems on lattice-isomorphisms between groups (Q1203994)
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scientific article; zbMATH DE number 124183
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple proof of Baer's and Sato's theorems on lattice-isomorphisms between groups |
scientific article; zbMATH DE number 124183 |
Statements
A simple proof of Baer's and Sato's theorems on lattice-isomorphisms between groups (English)
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18 February 1993
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A group \(G\) is said to be an \(M^*\)-group if all subgroups of \(G\) are quasinormal and \(G\) is quaternionfree. Using Iwasawa's characterization of \(M^*\)-groups the author gives an elegant and unified proof of the following theorem: If \(G\) is an \(M^*\)-group, then there exists an abelian group \(A\) such that the lattices of subgroups of \(A\) and \(G\) are isomorphic.
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quasinormal subgroups
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isomorphic lattices of subgroups
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\(M^*\)-groups
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abelian group
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