User m.z. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T21:06:50Z http://mathoverflow.net/feeds/user/11172 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/48434/names-of-finite-groups/48601#48601 Answer by M.Z. for Names of finite groups M.Z. 2010-12-08T00:17:23Z 2010-12-09T18:55:08Z <p>There is a useful convention to decorate some of the groups with an index which is the smallest $n$ for which the group can act transitively on $n$ points, i.e. embeds in $S_n$ as a transitive subgroup. The notation for $S_n, A_n, D_n, C_n$, your $Q_8$ and for example Mathieu groups $M_{11}, M_{12}, M_{22}$ (although not other sporadic simple groups) follow this pattern.</p> <p>Of course, there is also another convention to use the size of the group instead...</p> http://mathoverflow.net/questions/47952/proving-interesting-theorems-about-s-n-using-its-character-table/47953#47953 Answer by M.Z. for Proving interesting theorems about S_n using its character table. M.Z. 2010-12-01T22:12:58Z 2010-12-01T22:12:58Z <p>Because all the entries in the character table are integers and not just algebraic integers, you get that a proof that every permutation $\sigma$ of order $n$ is conjugate to all $\sigma^j$ for $j$ coprime to $n$. (Of course, one usually uses this in the opposite direction, to deduce that all entries are integers!)</p> http://mathoverflow.net/questions/47717/best-examples-of-physics-providing-insight-into-math/47719#47719 Answer by M.Z. for Best examples of physics providing insight into math M.Z. 2010-11-29T20:44:34Z 2010-11-29T20:44:34Z <p>I think one of the most intriguing examples is mirror symmetry: physical intuition has suggested formulae for the number of curves of a fixed genus ona Calabi-Yau 3-fold that mathematicians did not expect</p>