<html><head><title>[xgap] 4 Subgroup Lattices - Examples</title></head> <body text="#000000" bgcolor="#ffffff"> [<a href = "chapters.htm">Up</a>] [<a href ="C003S000.htm">Previous</a>] [<a href ="C005S000.htm">Next</a>] [<a href = "theindex.htm">Index</a>] <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:~> 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> [<a href = "chapters.htm">Up</a>] [<a href ="C003S000.htm">Previous</a>] [<a href ="C005S000.htm">Next</a>] [<a href = "theindex.htm">Index</a>] <P> <address>xgap manual<br>Mai 2003 </address></body></html>