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<p>We determine Jordan constants of groups <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2024_792_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="195" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{GL}_2(K),\textrm{SL}_2(K),\textrm{PGL}_2(K)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>GL</mtext> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <msub> <mtext>SL</mtext> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <msub> <mtext>PGL</mtext> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2024_792_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{PGL}_3(K)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>PGL</mtext> <mn>3</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for any given field <i>K</i> of characteristic 0.</p>

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Jordan constant of \(\textrm{PGL}_3(K)\)

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  • 发表日期：

    2025年1月8日

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  • Yijue Hu

摘要

We determine Jordan constants of groups \(\textrm{GL}_2(K),\textrm{SL}_2(K),\textrm{PGL}_2(K)\) GL 2 ( K ) , SL 2 ( K ) , PGL 2 ( K ) and \(\textrm{PGL}_3(K)\) PGL 3 ( K ) for any given field K of characteristic 0.