http://openproblemgarden.org/op/subgroup_formed_by_elements_of_order_dividing_n Comments for "Subgroup formed by elements of order dividing n" en http://openproblemgarden.org/op/subgroup_formed_by_elements_of_order_dividing_n#comment-7155 <p>it can be proved by a isomorphism between the solutions of x^n=1 in G and the solutions of the same eq in C (complex numbers).</p> Fri, 30 Mar 2012 20:21:03 +0200 Anonymous comment 7155 at http://openproblemgarden.org http://openproblemgarden.org/op/subgroup_formed_by_elements_of_order_dividing_n#comment-6869 <p>Iiyori, Nobuo; Yamaki, Hiroyoshi On a conjecture of Frobenius. Bull. Amer. Math. Soc. (N.S.) 25 (1991), no. 2, 413--416.</p> Wed, 01 Dec 2010 22:56:17 +0100 Anonymous comment 6869 at http://openproblemgarden.org http://openproblemgarden.org/op/subgroup_formed_by_elements_of_order_dividing_n#comment-6656 <p>Could you add a reference please?</p> Mon, 29 Jun 2009 11:01:02 +0200 Anonymous comment 6656 at http://openproblemgarden.org http://openproblemgarden.org/op/subgroup_formed_by_elements_of_order_dividing_n#comment-6655 <p>This conjecture has been proven.</p> Fri, 26 Jun 2009 22:52:31 +0200 Anonymous comment 6655 at http://openproblemgarden.org http://openproblemgarden.org/op/subgroup_formed_by_elements_of_order_dividing_n <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/frobenius_ferdinand_g">Frobenius</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> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp;</p> <p>Suppose <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is a finite group, and <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> is a positive integer dividing <img class="teximage" src="/files/tex/9882323e6d064bb1e86bb3b7374a36543d5050e6.png" alt="$ |G| $" />. Suppose that <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> has exactly <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> solutions to <img class="teximage" src="/files/tex/8b628f151c9773565ec91335d8790f49fd34b2a3.png" alt="$ x^{n} = 1 $" />. Does it follow that these solutions form a subgroup of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />?</p> </div> </tr></td> </table> </td> </tr> </table> Frobenius, Ferdinand G. order, dividing Group Theory http://openproblemgarden.org/op/subgroup_formed_by_elements_of_order_dividing_n#comment Mon, 28 Jan 2008 03:37:29 +0100 dlh12 732 at http://openproblemgarden.org