The Schur property for subgroup lattices of groups. (Q944207)
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scientific article; zbMATH DE number 5343878
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Schur property for subgroup lattices of groups. |
scientific article; zbMATH DE number 5343878 |
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The Schur property for subgroup lattices of groups. (English)
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12 September 2008
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By a well-known result of Schur's, if the centre \(Z(G)\) of a group \(G\) has finite index, then the commutator subgroup \(G'\) of \(G\) is finite. The main goal of this paper is to provide a lattice analogue of this result. It states that if a group \(G\) contains a modularly embedded subgroup of finite index, then there is a finite normal subgroup \(N\) of \(G\) such that the subgroup lattice of the quotient \(G/N\) is modular. Some interesting consequences of this theorem are also presented.
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modular lattices
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Schur theorem
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group coverings
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modularly embedded subgroups
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finite normal subgroups
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modular subgroup lattices
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groups covered by finitely many subgroups
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subgroups of finite index
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