http://openproblemgarden.org/op/gaos_theorem_for_nonabelian_groups Comments for "Gao's theorem for nonabelian groups" en http://openproblemgarden.org/op/gaos_theorem_for_nonabelian_groups <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/devos">DeVos</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/number_theory_0">Number Theory</a> » <a href="/category/combinatorial_number_theory">Combinatorial N.T.</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>For every finite multiplicative group <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, let <img class="teximage" src="/files/tex/675f61728ff327c6b49de455369ebc2a34b64ebb.png" alt="$ s(G) $" /> (<img class="teximage" src="/files/tex/f087e02524c8f1a8e91dbf877972349c0bd674f2.png" alt="$ s&#039;(G) $" />) denote the smallest integer <img class="teximage" src="/files/tex/ddaab6dc091926fb1da549195000491cefae85c1.png" alt="$ m $" /> so that every sequence of <img class="teximage" src="/files/tex/ddaab6dc091926fb1da549195000491cefae85c1.png" alt="$ m $" /> elements of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> has a subsequence of length <img class="teximage" src="/files/tex/05445ae864f7d95b09d4cfccd12539272c645aca.png" alt="$ &gt;0 $" /> (length <img class="teximage" src="/files/tex/9882323e6d064bb1e86bb3b7374a36543d5050e6.png" alt="$ |G| $" />) which has product equal to 1 in some order. </p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/91264d9b321ddb6a08656e574ccf314d9ebfa121.png" alt="$ s&#039;(G) = s(G) + |G| - 1 $" /> for every finite group <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. </div> </tr></td> </table> </td> </tr> </table> DeVos, Matt subsequence sum zero sum Number Theory Combinatorial Number Theory http://openproblemgarden.org/op/gaos_theorem_for_nonabelian_groups#comment Wed, 23 May 2007 00:33:55 +0200 mdevos 337 at http://openproblemgarden.org