http://openproblemgarden.org/op/hall_paige_conjecture Comments for "Hall-Paige conjecture" en http://openproblemgarden.org/op/hall_paige_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/marshall_hall">Hall</a>; <a href="/category/paige_lowell_j">Paige</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/group_theory">Group Theory</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>A <em>complete map</em> for a (multiplicative) group <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is a bijection <img class="teximage" src="/files/tex/1ae103f3b9131775806bb1f09ac5770a8fdf3f77.png" alt="$ \phi : G \rightarrow G $" /> so that the map <img class="teximage" src="/files/tex/24919cf3c41ca170b52915bda6f58338c41e9d46.png" alt="$ x \rightarrow x \phi (x) $" /> is also a bijection.</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; If <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is a finite group and the Sylow 2-subgroups of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> are either trivial or non-cyclic, then <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> has a complete map. </div> </tr></td> </table> </td> </tr> </table> Hall, Marshall Paige, Lowell J. complete map finite group latin square Group Theory http://openproblemgarden.org/op/hall_paige_conjecture#comment Sun, 21 Oct 2007 12:47:22 +0200 mdevos 682 at http://openproblemgarden.org