Maximal subgroups of free idempotent generated semigroups over the full linear monoid. (Q2862135)
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scientific article; zbMATH DE number 6226837
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximal subgroups of free idempotent generated semigroups over the full linear monoid. |
scientific article; zbMATH DE number 6226837 |
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14 November 2013
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free idempotent generated semigroups
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full linear monoids over division rings
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linear algebraic monoids
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maximal subgroups
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reductive monoids
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regular semigroups
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biordered sets of idempotents
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Maximal subgroups of free idempotent generated semigroups over the full linear monoid. (English)
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The authors show that the rank \(r\) component of the free idempotent generated semigroup of the biordered set of the full linear monoid of \(n\times n\) matrices over a division ring \(Q\) has a maximal subgroup isomorphic to the general linear group \(\text{GL}_r(Q)\), where \(n\) and \(r\) are positive integers with \(r<n/3\).
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