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- W2096421746 abstract "If a black box group is known to be isomorphic to an exceptional simple group of Lie type of (twisted) rank <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=greater-than 1> <mml:semantics> <mml:mrow> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>>1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, other than any <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=squared upper F 4 left-parenthesis q right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi /> <mml:mn>2</mml:mn> </mml:msup> <mml:mspace width=-.8pt /> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>4</mml:mn> </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>^2kern -.8pt F_4(q)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, over a field of known size, a Las Vegas algorithm is given to produce a constructive isomorphism. In view of its timing, this algorithm yields an upgrade of all known nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to any group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=squared upper F 4 left-parenthesis q right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi /> <mml:mn>2</mml:mn> </mml:msup> <mml:mspace width=-.8pt /> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>4</mml:mn> </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>^2kern -.8pt F_4(q)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> or <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=squared upper G 2 left-parenthesis q right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi /> <mml:mn>2</mml:mn> </mml:msup> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>2</mml:mn> </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>^2G_2(q)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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- W2096421746 date "2013-05-28" @default.
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- W2096421746 title "Black box exceptional groups of Lie type" @default.
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