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- W3103155265 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a linear group acting faithfully on a finite vector space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper V> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding=application/x-tex>V</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and assume that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis StartAbsoluteValue upper G EndAbsoluteValue comma StartAbsoluteValue upper V EndAbsoluteValue right-parenthesis equals 1> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>G</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mo>,</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>V</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>(|G|,|V|) =1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this paper we prove that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> admits a base of size two and that this estimate is sharp. This generalizes and strengthens several former results concerning base sizes of coprime linear groups. As a direct consequence, we answer a question of I. M. Isaacs in the affirmative." @default.
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- W3103155265 date "2015-12-15" @default.
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- W3103155265 title "Every coprime linear group admits a base of size two" @default.
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