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<div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap16.html">[Previous Chapter]</a>    <a href="chap18.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap17_mj.html">[MathJax on]</a></p>
<p><a id="X7A2144518112F830" name="X7A2144518112F830"></a></p>
<div class="ChapSects"><a href="chap17.html#X7A2144518112F830">17 <span class="Heading"> Generators and relators of groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap17.html#X7CFDEEC07F15CF82">17.1 <span class="Heading">  </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap17.html#X7F49A86A82EB2420">17.1-1 CayleyGraphOfGroupDisplay</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap17.html#X82C8B87287602BFA">17.1-2 IdentityAmongRelatorsDisplay</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap17.html#X78F2C5ED80D1C8DD">17.1-3 IsAspherical</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap17.html#X878938C3835871D7">17.1-4 PresentationOfResolution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap17.html#X7F71698178AF48DD">17.1-5 TorsionGeneratorsAbelianGroup</a></span>
</div></div>
</div>

<h3>17 <span class="Heading"> Generators and relators of groups</span></h3>

<p><a id="X7CFDEEC07F15CF82" name="X7CFDEEC07F15CF82"></a></p>

<h4>17.1 <span class="Heading">  </span></h4>

<p><a id="X7F49A86A82EB2420" name="X7F49A86A82EB2420"></a></p>

<h5>17.1-1 CayleyGraphOfGroupDisplay</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; CayleyGraphOfGroupDisplay</code>( <var class="Arg">G</var>, <var class="Arg">X</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; CayleyGraphOfGroupDisplay</code>( <var class="Arg">G</var>, <var class="Arg">X</var>, <var class="Arg">str</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a finite group <span class="SimpleMath">G</span> together with a subset <span class="SimpleMath">X</span> of <span class="SimpleMath">G</span>. It displays the corresponding Cayley graph as a .gif file. It uses the Mozilla web browser as a default to view the diagram. An alternative browser can be set using a second argument <span class="SimpleMath">str</span>="mozilla".</p>

<p>The argument <span class="SimpleMath">G</span> can also be a finite set of elements in a 

<p>This function requires

<p><strong<>aid=X7A2144518112F830name=X7A2144518112F830>/>/>

<p< id=X82C8B87287602BFA name"82C8B87287602BFA"<a<p

17.- h5

<div=func> class"unc"width=100"<< class">code=func>#;IdentityAmongRelatorsDisplaycode(< class"">R/>,< class"rg></var>)/td>tdclass"">&;function </></tr>/table></iv
< =func">< class=func"width="00%"<>< class=tdleft>codeclass=func>#;IdentityAmongRelatorsDisplay(var""><var,<varclass"rg"n/> < class=Arg>str/var> )/td>tdclass="tdright">( function )</td></tr></table></div>
<p>Inputs a free <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span> and <span =ContSS< />< =nocss>nbsp<>hrefh#>.- java.lang.StringIndexOutOfBoundsException: Range [139, 138) out of bounds for length 149

>  />

pb":/java.lang.StringIndexOutOfBoundsException: Range [58, 43) out of bounds for length 283

<p><a id="X78F2C5ED80D1C8DD" name="X78F2C5ED80D1C8DD"></a></p>

<h5>17.1

<div
<>    span=SimpleMath></pan    span=SimpleMath></pan>of in span=SimpleMath><span.  a   2dimensionalCW- span="K<span  to  presentation  the  <span ="SimpleMath>=/<span&;< class=SimpleMath></span&;< class=""><span./>

<p>a=X7F49A86A82EB2420name"">/a></p>

<p>Otherwise it returns "fail" and prints: Presentation is NOT piece-wise Euclidean non-positively curved. (In this case <span class="SimpleMath">K</span> may or may not have trivial second homotopy group

<p>Thediv="unc"><table =f java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 286

> =": "a="//h"<>/>,""a//2>/ < java.lang.StringIndexOutOfBoundsException: Range [189, 188) out of bounds for length 348

<p><a id="X878938C3835871D7" name="X878938C3835871D7"></a></p>

<h5>17.1-4 PresentationOfResolution</h5>

<div class="func"><table class="func" width="java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<> at leasttwo  ofareduced< class""></spanresolution< =SimpleMath"R/span> and returns a record <span class="SimpleMath">P</span> with components</p>


<ul>
<li><p><span class="SimpleMath">P.freeGroup</span> is a free group <span class="SimpleMath">F</span>,</p>

</li>
<lip<strong class="">Examples:/>/p>

</>
<lih5171- IdentityAmongRelatorsDisplayh5

<li
</ul>
p < =SimpleMath>G/>is  to< class=SimpleMath"</pan> java.lang.StringIndexOutOfBoundsException: Range [105, 104) out of bounds for length 420

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/java.lang.StringIndexOutOfBoundsException: Index 85 out of bounds for length 0

<p><a id="X7F71698178AF48DD" name="X7F71698178AF48DD"></a></p>

<h5>17.1-5 TorsionGeneratorsAbelianGroup

<java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<p>nputsanabelian group spanclass"SimpleMath"></> and returns a generating set <span class="SimpleMath">[x_1, ... ,x_n]</span> where no pair of generators have 

<p><strong class="button">Examples:SimpleMath>F</pan  a set span ="impleMath"R/> ofwordsin< class"SimpleMath"></>  performs test onthe- CW- span="impleMath></span> associated  thispresentation  the group <span class""GF//>&t<span ="impleMath><span&<class=SimpleMath>Fspan./>


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