Homomorphism from permutation group - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-23T12:04:25Z http://mathoverflow.net/feeds/question/54841 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54841/homomorphism-from-permutation-group Homomorphism from permutation group homo_n 2011-02-09T02:24:36Z 2011-02-09T08:19:48Z <p>In a group of permutations of \$n\$ elements, there are two permutations \$P_1\$ and \$P_2\$ such that \$P_2=P_1^e\$. \$P_1\$ and \$P_2\$ have the same order \$o\$: \$P_1^o = P_2^o\$. How can I find \$e\$? My idea is to use a homomorphism from permutations to integers modulo \$n\$ and solve the logarithm there, but how can I find correct mapping of \$P_1\$ and \$P_2\$ such that the order of elements is preserved? </p> <p>Clarification: \$n\$, \$P_1, P_2\$ and \$o\$ are known, \$e\$ is not known. Problem is to find \$e\$ by any means. It's an instance of DLP over permutation group. Homomorphism is just an idea, maybe it isn't the best solution.</p>