<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262009000100003</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[El teorema de Cayley revisitado]]></article-title>
<article-title xml:lang="es"><![CDATA[The theorem of Cayley revisited]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[MONTOYA]]></surname>
<given-names><![CDATA[J. ANDRÉS]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[Bucaramanga ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>15</day>
<month>06</month>
<year>2009</year>
</pub-date>
<pub-date pub-type="epub">
<day>15</day>
<month>06</month>
<year>2009</year>
</pub-date>
<volume>43</volume>
<numero>1</numero>
<fpage>19</fpage>
<lpage>34</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262009000100003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262009000100003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262009000100003&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[En este artículo probamos que no existe un N&isin; N tal que todo grupo finito puede ser embebido en GL\mathbbC( N).]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[In this paper we prove that there not exists N&isin; N such that any finite group can be embbeded into GL\mathbbC( N).]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Grupos finitos]]></kwd>
<kwd lng="en"><![CDATA[representaciones de grupos]]></kwd>
<kwd lng="en"><![CDATA[caracteres de grupos]]></kwd>
<kwd lng="es"><![CDATA[Finite groups]]></kwd>
<kwd lng="es"><![CDATA[linear representations]]></kwd>
<kwd lng="es"><![CDATA[group characters]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ 
<font size="2" face="verdana">

    <p>
<b>
<font size="4">
    <center>
El teorema de Cayley revisitado
</center>
</font>
</b>
</p>

    <p>
<b>
<font size="3">
    <center>
The theorem of Cayley revisited
</center>
</font>
</b>
</p>

    <p>
    <center>
J. ANDR&Eacute;S MONTOYA<sup>1</sup>
</center>
</p>

    <p>
<sup>1</sup>Universidad Industrial de Santander, Bucaramanga, Colombia. Email: <a href="mailto:juamonto@uis.edu.co">juamonto@uis.edu.co</a>
    <br>
</p>

<hr size="1">

    <p>
<b>
    ]]></body>
<body><![CDATA[<center>
Abstract
</center>
</b>
</p>

    <p>
En este art&iacute;culo probamos que no existe un <i>N&isin; <b>N</b></i> tal que todo grupo finito puede ser embebido en <i>GL<sub>\mathbbC</sub>( N)</i>.
</p>

    <p>
<b>
Key words:
</b>
Grupos finitos,
representaciones de grupos,
caracteres de grupos.
</p>

<hr size="1">

<i>2000 Mathematics Subject Classification: 20C15, 20C30.</i>

<hr size="1">

    <p>
<b>
    <center>
Resumen
</center>
</b>
</p>

    <p>
In this paper we prove that there not exists <i>N&isin; <b>N</b></i> such that any finite group can be embbeded into <i>GL<sub>\mathbbC</sub>( N)</i>.
</p>

    <p>
<b>
Palabras clave:
</b>
Finite groups,
linear representations,
group characters.
</p>

<hr size="1">

    <p>
Texto completo disponible en <a href="pdf/rcm/v43n1/v43n1a03.pdf">PDF</a>
</p>

<hr size="1">

    <p>
<b>
<font size="3">
References
</font>
</b>
</p>


    <!-- ref --><p>
[1] Fulton, W. & Harris, J., <i>Representation Theory: A first course</i>, Springer Verlag, N. Y., 1991.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000022&pid=S0034-7426200900010000300001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>
[2] Hodges, W., <i>Model Theory</i>, Cambridge University Press, Cambridge M. A., 1993.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000023&pid=S0034-7426200900010000300002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>
[3] Hungerford, T., <i>Algebra</i>, Springer Verlag, N. Y., 2000.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000024&pid=S0034-7426200900010000300003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>
[4] Kallman, R., `Every reasonably sized group is a subgroup of <i>S<sub>&omega;</sub>  </i>´, <i>Fundamenta Mathematicae</i> <i>164</i>,  (2000), 35-40.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000025&pid=S0034-7426200900010000300004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>
[5] Mauldin, R., ed., <i>The Scotish Book</i>, Birkhauser, Boston, 1981.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000026&pid=S0034-7426200900010000300005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><center>
<b>(Recibido en abril de 2008. Aceptado en enero de 2009)</b>
</center>
<hr size="1">

    <p>
Este art&iacute;culo se puede citar en <i>LaTeX</i> utilizando la siguiente referencia bibliogr&aacute;fica de <i>BibTeX</i>:
</p>
<code><font size="2">@ARTICLE{RCMv43n1a03,    <br>
 &nbsp;&nbsp;&nbsp; AUTHOR &nbsp;= {Montoya, J. Andr&eacute;s},    <br>
 &nbsp;&nbsp;&nbsp; TITLE &nbsp; = {{El teorema de Cayley revisitado}},    <br>
 &nbsp;&nbsp;&nbsp; JOURNAL = {Revista Colombiana de Matem&aacute;ticas},    <br>
&nbsp;&nbsp;&nbsp; YEAR &nbsp;&nbsp; = {2009},    ]]></body>
<body><![CDATA[<br>
&nbsp;&nbsp;&nbsp; volume &nbsp;= {43},    <br>
&nbsp;&nbsp;&nbsp; number &nbsp;= {1},    <br>
&nbsp;&nbsp;&nbsp; pages &nbsp; = {19-34}    <br>
}</font></code>

<hr size="1">
</font>
     ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fulton]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Harris]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Representation Theory: A first course]]></source>
<year>1991</year>
<publisher-name><![CDATA[Springer Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hodges]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<source><![CDATA[Model Theory]]></source>
<year>1993</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hungerford]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Algebra]]></source>
<year>2000</year>
<publisher-name><![CDATA[Springer Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kallman]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[`Every reasonably sized group is a subgroup of S_\omega ´]]></article-title>
<source><![CDATA[Fundamenta Mathematicae]]></source>
<year>2000</year>
<volume>164</volume>
<page-range>35-40</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mauldin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Scotish Book]]></source>
<year>1981</year>
<publisher-name><![CDATA[Birkhauser]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
