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<p>In this paper, we prove that the groups <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{GL}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>GL</mtext> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textrm{SL}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>SL</mtext> </math></EquationSource> </InlineEquation> over infinite fields of characteristics not equal to&#xa0;2 are <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((\forall \,\exists )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>∀</mo> <mspace width="0.166667em" /> <mo>∃</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-equivalent if and only if their dimensions coincide and the corresponding fields are <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((\forall \,\exists )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>∀</mo> <mspace width="0.166667em" /> <mo>∃</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-equivalent.</p>

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UNIVERSAL-EXISTENTIAL EQUIVALENCE OF LINEAR GROUPS

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • P. Pritup

摘要

In this paper, we prove that the groups \(\textrm{GL}\) GL and \(\textrm{SL}\) SL over infinite fields of characteristics not equal to 2 are \((\forall \,\exists )\) ( ∀ ∃ ) -equivalent if and only if their dimensions coincide and the corresponding fields are \((\forall \,\exists )\) ( ∀ ∃ ) -equivalent.