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 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>