| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/hap/www/SideLinks/About/table/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 19.6.2025 mit Größe 1 kB |
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <title>Summary</title> </head> <body style="color: rgb(0, 0, 0); background-color: rgb(204, 255, 255);" alink="#000099" link="#000099" vlink="#990099"> <big></big> <p><big>The table contains the following data for each of the 45 nonabelian groups G of order at most 30:</big></p> <ul> <big> <li>the order |G| and, where appropriate, name of G. </li> <li>a 3-presentation <tt><<u>x</u>|<u>r</u>|<u>s</u>></tt> for G. It is given using the convention that <ul plain=""> <li> the first generator in <tt><u>x</u></tt> is denoted by <tt>x</tt>, the second generator is denoted by <tt>y</tt>, the third generator (if exists) is denoted by <tt>z</tt>; </li> <li> the first relator in <tt><u>r</u></tt> is denoted by <tt>a</tt>, the second relator is denoted by <tt>b</tt>, the third by <tt>c</tt> and so on. </li> </ul> </li> <li> the rank dim<sub><img src="tiny_z.uc.gif"></sub><img src="pi.lc.gif"> of the free abelian group underling the module of identities <img src="pi.lc.gif">=<img src="pi.lc.gif"><sub>2</sub>K(<tt><u>x</u></tt>, <tt><u>r</u></tt>). </li> <li> a set <u>v</u> of elements in <img src="smearth.gif"><sub><tt><u>r</u></tt></sub> <b>Z</b>G that generates a <b>Z</b>G-submodule <img src="pi.lc.gif"><tt>'</tt> isomorphic to the <b>Z</b>G-module <img src="pi.lc.gif">. </li> <li> the integral homology group H<sub>n</sub>(G)=H<sub>n</sub>(G,<b>Z</b>) for n=1,2,3. </li> </big> </ul> <big> </big> <p><big><a href="help.html">How to use the table?</a> </big></p> <p><big><a href="table.html">The main table</a></big></p> </body> </html>
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2026-05-26