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• W1966602092 abstract "We show that the rank <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=r> <mml:semantics> <mml:mi>r</mml:mi> <mml:annotation encoding=application/x-tex>r</mml:annotation> </mml:semantics> </mml:math> </inline-formula> component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n times n> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>×<!-- × --></mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>n times n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrices over a division ring <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Q> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding=application/x-tex>Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has maximal subgroup isomorphic to the general linear group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G upper L Subscript r Baseline left-parenthesis upper Q right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>r</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>GL_r(Q)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=r> <mml:semantics> <mml:mi>r</mml:mi> <mml:annotation encoding=application/x-tex>r</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are positive integers with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=r greater-than n slash 3> <mml:semantics> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>></mml:mo> <mml:mi>n</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>r > n/3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W1966602092 date "2013-07-24" @default.
• W1966602092 modified "2023-10-17" @default.
• W1966602092 title "Maximal subgroups of free idempotent generated semigroups over the full linear monoid" @default.
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