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<h1>4 Subgroup Lattices - Examples</h1><p>
<P>
<H3>Sections</H3>
<oL>
<li> <A HREF="C004S001.htm">The Subgroup Lattice of the Dihedral Group of Order 8</a>
<li> <A HREF="C004S002.htm">A Partial Subgroup Lattice of the Symmetric Group on 6 Points</a>
<li> <A HREF="C004S003.htm">A Partial Subgroup Lattice of the Cavicchioli Group</a>
<li> <A HREF="C004S004.htm">A Partial Subgroup Lattice of the Trefoil Knot Group</a>
<li> <A HREF="C004S005.htm">A Partial Subgroup Lattice of a Finitely Presented Group</a>
<li> <A HREF="C004S006.htm">A Partial Subgroup Lattice of a Space Group</a>
</ol><p>
<p>
XGAP provides a graphical interface to the  lattice or a partial lattice
of subgroups of groups.  For finitely  presented groups it gives you easy
access for example to the low index, prime quotient and Reidemeister-Schreier
algorithms in order to build a partial  lattice interactively.  For other
types of groups  it provides easy access to  many of  the group functions
(for example, the normalizer, normal subgroups, and Sylow subgroups).
<p>
This chapter explains  how to use this  interface by way of examples.  
Chapter  <a href="C005S000.htm">Subgroup  Lattices - Systematic  Description</a> gives
details about the   various  options and menus available.    These two
chapters  will not  describe how to  write  your own programs using the
graphic extensions supplied by XGAP, see chapters <a href="C006S000.htm">Graphic Sheets - Basic graphic operations</a> to <a href="C009S000.htm">Graphic Graphs</a> for details.
<p>
It is assumed that you have already started XGAP.  On most systems you
do this by typing
<p>
<pre>
user@host:~&gt; xgap 
</pre>
<p>
on  the  command line.   Ask your  system administrator  if this does not
work.  This   command  will create   a new window,   the so called <font face="Gill Sans,Helvetica,Arial">GAP</font>
window, in which <font face="Gill Sans,Helvetica,Arial">GAP</font> is awaiting your input.   Depending on the window
system and window manager  you use, placing a new  window on your  screen
might be  done  automatically or might  require  you to use the  mouse to
choose a position for the  window and pressing the  left mouse button  to
place the window.
<p>
The small arrow   or cross you see on   your screen is  called a pointer.
Although the device used to move this pointer can be anything, a mouse, a
track ball, a glide-pad, or even something as exotic as a rat, we will use
the term mouse to refer to this pointer device.
<p>
In case that some computation takes longer than expected, for instance
the low index and the prime quotient can be quite time consuming, you
can always interrupt a computation by making the <font face="Gill Sans,Helvetica,Arial">GAP</font> window active
and pressing <var>CTRL-C</var> or selecting <code>Interrupt</code> in the <code>Run</code> menu.
Again, making a window active is system and window manager dependent.
In most cases you either have to move the pointer inside the <font face="Gill Sans,Helvetica,Arial">GAP</font>
window or you have to click on the title bar of the <font face="Gill Sans,Helvetica,Arial">GAP</font> window.
<p>
Note that for each of the following examples there is a small <font face="Gill Sans,Helvetica,Arial">GAP</font>
script in the <code>examples</code> subdirectory of the XGAP home directory
which contains the necessary commands. However we consider it better
for learning XGAP in a first time session if you type the commands
by hand as suggested in the next few sections of this manual.
<p>
<p>
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<P>
<address>xgap manual<br>Mai 2003
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