Jump to navigation Jump to search

General

Display information for equation id:math.224426.2 on revision:224426

* Page found: Special linear group (eq math.224426.2)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: bdd89181fdfec8b4d4cf23e726682587

TeX (original user input):

\operatorname{Alt}(3) \cong [\operatorname{GL}(2, \mathbf{F}_2),\operatorname{GL}(2, \mathbf{F}_2)] < \operatorname{E}(2, \mathbf{F}_2) = \operatorname{SL}(2, \mathbf{F}_2) = \operatorname{GL}(2, \mathbf{F}_2) \cong \operatorname{Sym}(3),

TeX (checked):

\operatorname {Alt} (3)\cong [\operatorname {GL} (2,\mathbf {F} _{2}),\operatorname {GL} (2,\mathbf {F} _{2})]<\operatorname {E} (2,\mathbf {F} _{2})=\operatorname {SL} (2,\mathbf {F} _{2})=\operatorname {GL} (2,\mathbf {F} _{2})\cong \operatorname {Sym} (3),

LaTeXML (experimental; uses MathML) rendering

MathML (11.484 KB / 1.585 KB) :

Alt โก ( 3 ) โ‰… [ GL โก ( 2 , ๐… 2 ) , GL โก ( 2 , ๐… 2 ) ] < E โก ( 2 , ๐… 2 ) = SL โก ( 2 , ๐… 2 ) = GL โก ( 2 , ๐… 2 ) โ‰… Sym โก ( 3 ) , Alt 3 GL 2 subscript ๐… 2 GL 2 subscript ๐… 2 normal-E 2 subscript ๐… 2 SL 2 subscript ๐… 2 GL 2 subscript ๐… 2 Sym 3 {\displaystyle\operatorname{Alt}(3)\cong[\operatorname{GL}(2,{\mathbf{F}}_{2})% ,\operatorname{GL}(2,{\mathbf{F}}_{2})]<\operatorname{E}(2,{\mathbf{F}}_{2})=% \operatorname{SL}(2,{\mathbf{F}}_{2})=\operatorname{GL}(2,{\mathbf{F}}_{2})% \cong\operatorname{Sym}(3),}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\operatorname{Alt}(3)\cong[\operatorname{GL}(2,{\mathbf{F}}_{2})%&#10;,\operatorname{GL}(2,{\mathbf{F}}_{2})]&lt;\operatorname{E}(2,{\mathbf{F}}_{2})=%&#10;\operatorname{SL}(2,{\mathbf{F}}_{2})=\operatorname{GL}(2,{\mathbf{F}}_{2})%&#10;\cong\operatorname{Sym}(3),}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.61" xref="p1.1.m1.1.61.cmml">
      <mrow id="p1.1.m1.1.61a" xref="p1.1.m1.1.61.cmml">
        <mrow id="p1.1.m1.1.61.2.2" xref="p1.1.m1.1.61.2.1.cmml">
          <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">Alt</mo>
          <mo id="p1.1.m1.1.61.2.2a" xref="p1.1.m1.1.61.2.1.cmml">โก</mo>
          <mrow id="p1.1.m1.1.61.2" xref="p1.1.m1.1.61.2.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.61.2.1.cmml">(</mo>
            <mn id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">3</mn>
            <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.61.2.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">โ‰…</mo>
        <mrow id="p1.1.m1.1.61.3" xref="p1.1.m1.1.61.3.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.8">[</mo>
          <mrow id="p1.1.m1.1.61.3.2.2" xref="p1.1.m1.1.61.3.2.1.cmml">
            <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">GL</mo>
            <mo id="p1.1.m1.1.61.3.2.2a" xref="p1.1.m1.1.61.3.2.1.cmml">โก</mo>
            <mrow id="p1.1.m1.1.61.3.2" xref="p1.1.m1.1.61.3.2.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.61.3.2.1.cmml">(</mo>
              <mn id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">2</mn>
              <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.61.3.2.1.cmml">,</mo>
              <msub id="p1.1.m1.1.61.3.2.2.1" xref="p1.1.m1.1.61.3.2.1.cmml">
                <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">๐…</mi>
                <mn id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">2</mn>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.16" xref="p1.1.m1.1.61.3.2.1.cmml">)</mo>
            </mrow>
          </mrow>
          <mo id="p1.1.m1.1.17">,</mo>
          <mrow id="p1.1.m1.1.61.3.3.2" xref="p1.1.m1.1.61.3.3.1.cmml">
            <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">GL</mo>
            <mo id="p1.1.m1.1.61.3.3.2a" xref="p1.1.m1.1.61.3.3.1.cmml">โก</mo>
            <mrow id="p1.1.m1.1.61.3.3" xref="p1.1.m1.1.61.3.3.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.20" xref="p1.1.m1.1.61.3.3.1.cmml">(</mo>
              <mn id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">2</mn>
              <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.61.3.3.1.cmml">,</mo>
              <msub id="p1.1.m1.1.61.3.3.2.1" xref="p1.1.m1.1.61.3.3.1.cmml">
                <mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">๐…</mi>
                <mn id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">2</mn>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.25" xref="p1.1.m1.1.61.3.3.1.cmml">)</mo>
            </mrow>
          </mrow>
          <mo stretchy="false" id="p1.1.m1.1.26">]</mo>
        </mrow>
        <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">&lt;</mo>
        <mrow id="p1.1.m1.1.61.4.2" xref="p1.1.m1.1.61.4.1.cmml">
          <mo id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">E</mo>
          <mo id="p1.1.m1.1.61.4.2a" xref="p1.1.m1.1.61.4.1.cmml">โก</mo>
          <mrow id="p1.1.m1.1.61.4" xref="p1.1.m1.1.61.4.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.29" xref="p1.1.m1.1.61.4.1.cmml">(</mo>
            <mn id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">2</mn>
            <mo id="p1.1.m1.1.31" xref="p1.1.m1.1.61.4.1.cmml">,</mo>
            <msub id="p1.1.m1.1.61.4.2.1" xref="p1.1.m1.1.61.4.1.cmml">
              <mi id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">๐…</mi>
              <mn id="p1.1.m1.1.33.1" xref="p1.1.m1.1.33.1.cmml">2</mn>
            </msub>
            <mo stretchy="false" id="p1.1.m1.1.34" xref="p1.1.m1.1.61.4.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">=</mo>
        <mrow id="p1.1.m1.1.61.5.2" xref="p1.1.m1.1.61.5.1.cmml">
          <mo id="p1.1.m1.1.37" xref="p1.1.m1.1.37.cmml">SL</mo>
          <mo id="p1.1.m1.1.61.5.2a" xref="p1.1.m1.1.61.5.1.cmml">โก</mo>
          <mrow id="p1.1.m1.1.61.5" xref="p1.1.m1.1.61.5.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.38" xref="p1.1.m1.1.61.5.1.cmml">(</mo>
            <mn id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">2</mn>
            <mo id="p1.1.m1.1.40" xref="p1.1.m1.1.61.5.1.cmml">,</mo>
            <msub id="p1.1.m1.1.61.5.2.1" xref="p1.1.m1.1.61.5.1.cmml">
              <mi id="p1.1.m1.1.41" xref="p1.1.m1.1.41.cmml">๐…</mi>
              <mn id="p1.1.m1.1.42.1" xref="p1.1.m1.1.42.1.cmml">2</mn>
            </msub>
            <mo stretchy="false" id="p1.1.m1.1.43" xref="p1.1.m1.1.61.5.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.44" xref="p1.1.m1.1.44.cmml">=</mo>
        <mrow id="p1.1.m1.1.61.6.2" xref="p1.1.m1.1.61.6.1.cmml">
          <mo id="p1.1.m1.1.46" xref="p1.1.m1.1.46.cmml">GL</mo>
          <mo id="p1.1.m1.1.61.6.2a" xref="p1.1.m1.1.61.6.1.cmml">โก</mo>
          <mrow id="p1.1.m1.1.61.6" xref="p1.1.m1.1.61.6.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.47" xref="p1.1.m1.1.61.6.1.cmml">(</mo>
            <mn id="p1.1.m1.1.48" xref="p1.1.m1.1.48.cmml">2</mn>
            <mo id="p1.1.m1.1.49" xref="p1.1.m1.1.61.6.1.cmml">,</mo>
            <msub id="p1.1.m1.1.61.6.2.1" xref="p1.1.m1.1.61.6.1.cmml">
              <mi id="p1.1.m1.1.50" xref="p1.1.m1.1.50.cmml">๐…</mi>
              <mn id="p1.1.m1.1.51.1" xref="p1.1.m1.1.51.1.cmml">2</mn>
            </msub>
            <mo stretchy="false" id="p1.1.m1.1.52" xref="p1.1.m1.1.61.6.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.53" xref="p1.1.m1.1.53.cmml">โ‰…</mo>
        <mrow id="p1.1.m1.1.61.7.2" xref="p1.1.m1.1.61.7.1.cmml">
          <mo id="p1.1.m1.1.56" xref="p1.1.m1.1.56.cmml">Sym</mo>
          <mo id="p1.1.m1.1.61.7.2a" xref="p1.1.m1.1.61.7.1.cmml">โก</mo>
          <mrow id="p1.1.m1.1.61.7" xref="p1.1.m1.1.61.7.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.57" xref="p1.1.m1.1.61.7.1.cmml">(</mo>
            <mn id="p1.1.m1.1.58" xref="p1.1.m1.1.58.cmml">3</mn>
            <mo stretchy="false" id="p1.1.m1.1.59" xref="p1.1.m1.1.61.7.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.61b" xref="p1.1.m1.1.61.cmml">,</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.61.cmml" xref="p1.1.m1.1.61">
        <and id="p1.1.m1.1.61a.cmml" xref="p1.1.m1.1.61"/>
        <apply id="p1.1.m1.1.61b.cmml" xref="p1.1.m1.1.61">
          <approx id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
          <apply id="p1.1.m1.1.61.2.1.cmml" xref="p1.1.m1.1.61.2.2">
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">Alt</ci>
            <cn type="integer" id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">3</cn>
          </apply>
          <interval closure="closed" id="p1.1.m1.1.61.3.1.cmml" xref="p1.1.m1.1.61.3">
            <apply id="p1.1.m1.1.61.3.2.1.cmml" xref="p1.1.m1.1.61.3.2.2">
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">GL</ci>
              <cn type="integer" id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">2</cn>
              <apply id="p1.1.m1.1.61.3.2.2.1.cmml" xref="p1.1.m1.1.61.3.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.61.3.2.2.1.1.cmml">subscript</csymbol>
                <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">๐…</ci>
                <cn type="integer" id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">2</cn>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.61.3.3.1.cmml" xref="p1.1.m1.1.61.3.3.2">
              <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">GL</ci>
              <cn type="integer" id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">2</cn>
              <apply id="p1.1.m1.1.61.3.3.2.1.cmml" xref="p1.1.m1.1.61.3.3.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.61.3.3.2.1.1.cmml">subscript</csymbol>
                <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">๐…</ci>
                <cn type="integer" id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">2</cn>
              </apply>
            </apply>
          </interval>
        </apply>
        <apply id="p1.1.m1.1.61c.cmml" xref="p1.1.m1.1.61">
          <lt id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27"/>
          <share href="#p1.1.m1.1.61.3.cmml" id="p1.1.m1.1.61d.cmml" xref="p1.1.m1.1.61"/>
          <apply id="p1.1.m1.1.61.4.1.cmml" xref="p1.1.m1.1.61.4.2">
            <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">normal-E</ci>
            <cn type="integer" id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">2</cn>
            <apply id="p1.1.m1.1.61.4.2.1.cmml" xref="p1.1.m1.1.61.4.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.61.4.2.1.1.cmml">subscript</csymbol>
              <ci id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">๐…</ci>
              <cn type="integer" id="p1.1.m1.1.33.1.cmml" xref="p1.1.m1.1.33.1">2</cn>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.61e.cmml" xref="p1.1.m1.1.61">
          <eq id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35"/>
          <share href="#p1.1.m1.1.61.4.cmml" id="p1.1.m1.1.61f.cmml" xref="p1.1.m1.1.61"/>
          <apply id="p1.1.m1.1.61.5.1.cmml" xref="p1.1.m1.1.61.5.2">
            <ci id="p1.1.m1.1.37.cmml" xref="p1.1.m1.1.37">SL</ci>
            <cn type="integer" id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">2</cn>
            <apply id="p1.1.m1.1.61.5.2.1.cmml" xref="p1.1.m1.1.61.5.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.61.5.2.1.1.cmml">subscript</csymbol>
              <ci id="p1.1.m1.1.41.cmml" xref="p1.1.m1.1.41">๐…</ci>
              <cn type="integer" id="p1.1.m1.1.42.1.cmml" xref="p1.1.m1.1.42.1">2</cn>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.61g.cmml" xref="p1.1.m1.1.61">
          <eq id="p1.1.m1.1.44.cmml" xref="p1.1.m1.1.44"/>
          <share href="#p1.1.m1.1.61.5.cmml" id="p1.1.m1.1.61h.cmml" xref="p1.1.m1.1.61"/>
          <apply id="p1.1.m1.1.61.6.1.cmml" xref="p1.1.m1.1.61.6.2">
            <ci id="p1.1.m1.1.46.cmml" xref="p1.1.m1.1.46">GL</ci>
            <cn type="integer" id="p1.1.m1.1.48.cmml" xref="p1.1.m1.1.48">2</cn>
            <apply id="p1.1.m1.1.61.6.2.1.cmml" xref="p1.1.m1.1.61.6.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.61.6.2.1.1.cmml">subscript</csymbol>
              <ci id="p1.1.m1.1.50.cmml" xref="p1.1.m1.1.50">๐…</ci>
              <cn type="integer" id="p1.1.m1.1.51.1.cmml" xref="p1.1.m1.1.51.1">2</cn>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.61i.cmml" xref="p1.1.m1.1.61">
          <approx id="p1.1.m1.1.53.cmml" xref="p1.1.m1.1.53"/>
          <share href="#p1.1.m1.1.61.6.cmml" id="p1.1.m1.1.61j.cmml" xref="p1.1.m1.1.61"/>
          <apply id="p1.1.m1.1.61.7.1.cmml" xref="p1.1.m1.1.61.7.2">
            <ci id="p1.1.m1.1.56.cmml" xref="p1.1.m1.1.56">Sym</ci>
            <cn type="integer" id="p1.1.m1.1.58.cmml" xref="p1.1.m1.1.58">3</cn>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\operatorname{Alt}(3)\cong[\operatorname{GL}(2,{\mathbf{F}}_{2})%
,\operatorname{GL}(2,{\mathbf{F}}_{2})]&lt;\operatorname{E}(2,{\mathbf{F}}_{2})=%
\operatorname{SL}(2,{\mathbf{F}}_{2})=\operatorname{GL}(2,{\mathbf{F}}_{2})%
\cong\operatorname{Sym}(3),}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (18.017 KB / 5.25 KB) :

upper A l t left-parenthesis 3 right-parenthesis approximately-equals left-bracket upper G upper L left-parenthesis 2 comma bold upper F 2 right-parenthesis comma upper G upper L left-parenthesis 2 comma bold upper F 2 right-parenthesis right-bracket less-than normal upper E left-parenthesis 2 comma bold upper F 2 right-parenthesis equals upper S upper L left-parenthesis 2 comma bold upper F 2 right-parenthesis equals upper G upper L left-parenthesis 2 comma bold upper F 2 right-parenthesis approximately-equals upper S y m left-parenthesis 3 right-parenthesis comma

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

[ERROR] java.lang.IllegalArgumentException: java.lang.ClassCastException@5246835d

Translation to Mathematica

In Mathematica:

[ERROR] java.lang.IllegalArgumentException: java.lang.ClassCastException@5246835d

Similar pages

Calculated based on the variables occurring on the entire Special linear group page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results