Quelle  chap0_mj.html   Sprache: HTML

<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<script type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (tut) - Contents</title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap0"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap0.html">[MathJax off]</a></p>
<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">

<h1>GAP — A Tutorial</h1>

<p>Release 4.15.1, 2025-10-18</p>

</div>
<p><b>The GAP Group
    
    
  </b>
<br />Email: <span class="URL"><a href="mailto:support@gap-system.org">support@gap-system.org</a></span>
<br />Homepage: <span class="URL"><a href="https://www.gap-system.org">https://www.gap-system.org</a></span>
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>Copyright © (1987-2025) for the core part of the <strong class="pkg">GAP<<?ml version=1.0" encoding="UTF-8"?>

<p>Most parts of this distribution, including the core part of the <strong class="pkg">GAP</strong> system are distributed under the terms of the GNU General Public License, see <span class="URL"><a href="https://www.gnu.org/licenses/gpl.html">https://www.gnu.org/licenses/gpl.html</a></span> or the file <code class="file">GPL</code> in the <code

<p>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p><strong class="pkg">GAP</strong> is developed over a long time and has many authors and contributors. More detailed information can be found in <span class<cript src="manualj"type="ext/>/script

<<iv =chlinktop"<=chlink1"Goto  />ahref=".></a><a href"."1<a>< =c.><a  < =chap3_mjhtml>3</><a =chap4_mjhtml"4<a  ahref"."5<a>  a =chap6_mj."><a <a href="."7/><a ="hap8_mj.html"8</>ahref"chapBib_mjhtml">Bib<a  a ="html>nd<a></div>

<div java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<Contentsaid=contents" "contents><a<h3java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54

<div class="ContChap"><a href="chap1_mj.html#X874E1D45845007FE">1 <span class="Heading">Preface</span></a<>a ="7"nameX7D2C85EC87DD46E5<a>/>
<div class=C"<span =tocline"><class="" /pan< href"hap1_mj.html#">11<span =Heading"The strong class="pkg">GAP</strong> System</span></a>
</span>
</div>
<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
</span>
</div>
</div
<class=""<=chap2_mj.tml#"2 <pan ="Heading>A  with strong ="pkg"<strong</>/ajava.lang.StringIndexOutOfBoundsException: Range [152, 153) out of bounds for length 152
<java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 209
<span>
</div>
<div class="ContSect"><span br />Homepage: <span class="URLhref="https:/wwwg-system.org>:/ww.java.lang.StringIndexOutOfBoundsException: Index 86 out of bounds for length 62
java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 7
<div>
<div class="ContSect"><span class="tocline"><span class="nocss"> java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X86CA8242832F5F71">
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 0
<< class=contents">
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
</java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
<d>
<lass"ontSect"<pan class=ocline">s class=""> />< =c.X796E055D86856B42"2.7<pan "eading>Functions/pan<a>
</ivjava.lang.StringIndexOutOfBoundsException: Range [6, 7) out of bounds for length 6
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 7
/java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 7
/>
<div/java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 7
</java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 7
</div>
</div>
<div class="ContChap"><a href="chap3_mj.html#X7863DAFD78E5DFB6/span>
d class=ContSect"><pan classt">< class"" <span<href=chap3_mj.tml#">31 <pan ""> Lists<span>/ajava.lang.StringIndexOutOfBoundsException: Index 167 out of bounds for length 167
<span>
</div>
<div class=div>
</span>
</div>
<div class="ContSect<class=ContSect">span =tocline">span =nocss">n;<span>< "chap2_mjh#"2.6 <span class="Heading">Objects vs. Elements</span></a>
<>
</<iv class"ContSect">span class=tocline>span =nocss">nbsp;/>ahref=hap2_mj.html#">2. <spanclass="Heading"About Functions/pan<a>
<div class="ContSect"><span class="tocline"><span class</span>
</span>
</div>
<div class="ContSect"><span class="tocline">
</span>
</div>
<divclass"<span =tocline>span class""&;</span>a =chap3_mj.tml#java.lang.StringIndexOutOfBoundsException: Range [119, 117) out of bounds for length 175
</span>
</div>
<div class="ContSect"><span class="tocline"><span span>
</<div c"ContChap"<href="chap3_mj.tml#"> <spanclass=Heading" and <span><a>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </panjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
<span
</div>
<div class="java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 7
/java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 7
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </spanjava.lang.StringIndexOutOfBoundsException: Range [7, 8) out of bounds for length 7
</span>
</div>
</div>
<div class="ContChap"><a href="chap4_mj.html#java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 7
< "ContSect><pan =t"<panclass"">&;/>a =c.X7"41<span class="Writing Functions/span<ajava.lang.StringIndexOutOfBoundsException: Range [173, 174) out of bounds for length 173
</span>
</div>
<div class="ContSect"><span class="tocline"><s>
<n>
</div>
<java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 171
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><<div class="ContSect"><span class="tocline"><span class="nocss"> </java.lang.StringIndexOutOfBoundsException: Range [0, 76) out of bounds for length 7
</span>
</div>
<div class="ContSect"><span class="java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 7
/>
<>
</div>
<divnocss"> </span><a href="chap5_mj.html#X7FFD731684606BC6">5.5 <span class="Heading">Nice Monomorphisms</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X85ED46007CED6191">5.1 <span class="Heading">Permutation groups</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X8493BB7D7ECB5AB2">5.2 <span class="Heading">Actions of Groups</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X8742F6A083ADE513">5.3 <span class="Heading">Subgroups as Stabilizers</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X8131EE9182385680">5.4 <span class="Heading">Group Homomorphisms by Images</span>java.lang.StringIndexOutOfBoundsException: Index 203 out of bounds for length 203
<>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7FFD731684606BC6">5.5 <span class="Heading">Nice Monomorphisms>by<href=https://java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 112
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X84579FB48474079C">5.6 <span class="Heading">Further Information about Groups and Homomorphisms</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap6_mj.html#X853484B982F1DF96">6 <span class="Heading">Vector Spaces and Algebras</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7DAD6700787EC845">6.1 <span class="Heading">Vector Spaces</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7DDBF6F47A2E021C">6.2 <span class="Heading">Algebras</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X843A8D6F7A7592B5">6.3 <span class="Heading">Further Information about Vector Spaces and Algebras</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap7_mj.html#X7BAF69417BB925F6">7 <span class="Heading">Domains</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7D94C6F07ACEA397">7.1 <span class="Heading">Domains as Sets</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X81F376D67BA4F5EB">7.2 <span class="Heading">Algebraic Structure</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7E8D59018638925F">7.3 <span class="Heading">Notions of Generation</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X85AB533B7DE21C8B">7.4 <span class="Heading">Domain Constructors</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X849B1C5F8136F3A9">7.5 <span class="Heading">Forming Closures of Domains</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7EA77DE17DD8A231">7.6 <span class="Heading">Changing the Structure</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X8318352D7B5F19BA">7.7 <span class="Heading">Subdomains</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7C83996381F67238">7.8 <span class="Heading">Further Information about Domains</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap8_mj.html#X7AEED9AB824CD4DA">8 <span class="Heading">Operations and Methods</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X7C701DBF7BAE649A">8.1 <span class="Heading">Attributes</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X81C430C37B2F16D8">8.2 <span class="Heading">Properties and Filters</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X85CC8C167A280043">8.3 <span class="Heading">Immediate and True Methods</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X7DF5DBF9868B02C0">8.4 <span class="Heading">Operations and Method Selection</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
<br />
</div>

<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>