<html><head><title>[xgap] 5.13 GraphicSubgroupLattice for FpGroups, Information Menu</title></head> <body text="#000000" bgcolor="#ffffff"> [<a href = "C005S000.htm">Up</a>] [<a href ="C005S012.htm">Previous</a>] [<a href ="C006S000.htm">Next</a>] [<a href = "theindex.htm">Index</a>] <h1>5.13 GraphicSubgroupLattice for FpGroups, Information Menu</h1><p> <p> Placing the pointer inside a vertex (selected or not) and pressing the <strong>right</strong> mouse button pops up the ``Information'' menu. Clicking on any of the text lines will compute the corresponding property of the subgroup <var>u</var> associated with this vertex. Clicking on <code>close</code> will close the ``Information'' menu. <p> <a name = "SSEC1"></a> <li><code>Index</code> <p> displays the index of <var>u</var> in the whole group. <p> <a name = "SSEC2"></a> <li><code>IsNormal</code> <p> checks if <var>u</var> is normal in the whole group. <p> <a name = "SSEC3"></a> <li><code>IsFpGroup</code> <p> checks if <var>u</var> is a finitely presented group. Note that a subgroup of a finitely presented group that is defined by a coset table or as kernel of an epimorphism is <strong>not</strong> automatically known to <font face="Gill Sans,Helvetica,Arial">GAP</font> as a finitely presented group. This means, that certain algorithms can not be applied. Use <code>IsomorphismFpGroup</code> (see <a href="../../../doc/htm/ref/C045S010.htm#SSEC1">IsomorphismFpGroup</a> in the <font face="Gill Sans,Helvetica,Arial">GAP</font> reference manual) to calculate a finitely presented group and an isomorphism onto it, if some calculation does not work automatically. <p> <a name = "SSEC4"></a> <li><code>Abelian Invariants</code> <p> computes and displays the abelian invariants of <var>u</var>. <p> <a name = "SSEC5"></a> <li><code>Coset Table</code> <p> computes a coset table for <var>u</var>. <p> <a name = "SSEC6"></a> <li><code>IsomorphismFpGroup</code> <p> computes a finitely presented group that is isomorphic to <var>u</var> and displays the number of generators and relators of it. <p> <a name = "SSEC7"></a> <li><code>Factor Fp Group</code> <p> computes the factor group of the whole group by <var>u</var>, if <var>u</var> is normal. <p> Note that the exact result of all these information displays is stored in the global variable <code>LastResultOfInfoDisplay</code> after each operation. So you can access this easily from the <font face="Gill Sans,Helvetica,Arial">GAP</font> command prompt. It is also returned as <code>last</code> value. <p> <p> [<a href = "C005S000.htm">Up</a>] [<a href ="C005S012.htm">Previous</a>] [<a href ="C006S000.htm">Next</a>] [<a href = "theindex.htm">Index</a>] <P> <address>xgap manual<br>Mai 2003 </address></body></html>
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