The Symmetry of Steiner System S(5,8,24) - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T01:48:32Z http://mathoverflow.net/feeds/question/81946 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81946/the-symmetry-of-steiner-system-s5-8-24 The Symmetry of Steiner System S(5,8,24) Q'_'Q 2011-11-26T13:41:19Z 2011-11-29T17:03:56Z <p>The group of automorphisms of S(5,8,24), M_{24}, is 5-transitive. </p> <p>Other than Symmetric groups are there any other 5-transitive groups?</p> <p>If not, would it be correct to say S(5,8,24) is the most symmetric object (not counting trivially obvious objects like the graph K_{n}) in existence?</p> http://mathoverflow.net/questions/81946/the-symmetry-of-steiner-system-s5-8-24/82199#82199 Answer by Tom De Medts for The Symmetry of Steiner System S(5,8,24) Tom De Medts 2011-11-29T17:03:56Z 2011-11-29T17:03:56Z <p>If you're only interested in finite permutation groups, then Koen S has given you the answer you needed. If you allow infinite objects, then there are much more symmetric objects than S(5,8,24).</p> <p>In fact, there is a notion of "highly transitive permutation groups": these are permutation groups (acting on an infinite set \$\Omega\$) that are \$k\$-transitive for every natural number \$k\$. Quite often, model-theoretic tools are used to construct non-obvious examples of such groups (e.g. using Fraïssé limits).</p>