minimal index of proper subgroups of PSL(r,q) - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T05:52:59Z http://mathoverflow.net/feeds/question/44735 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/44735/minimal-index-of-proper-subgroups-of-pslr-q minimal index of proper subgroups of PSL(r,q) chemaida 2010-11-03T21:59:02Z 2010-11-04T09:17:15Z <p>By a Classification of Dickson everysubgroup of PSL(2,p) has index at least p+1</p> <p>is there an easy proof with out this classification?? </p> <p>What can be said about the minimal index of subgroups PSL(r,q)?? There is a classification of subgroups of PSL(3,p) by Bloom , even for this list i could not calculate all the indexes.</p> <p>Any references are welcome</p> http://mathoverflow.net/questions/44735/minimal-index-of-proper-subgroups-of-pslr-q/44794#44794 Answer by Derek Holt for minimal index of proper subgroups of PSL(r,q) Derek Holt 2010-11-04T09:17:15Z 2010-11-04T09:17:15Z <p>The first published proof that the index of a subgroup of PSL\$(2,p)\$ is at least \$p+1\$ for primes \$p \ge 13\$ is in:</p> <p>C. Jordan, "Note sur les equations modulaires", C.R. Acad. Sci. Paris 66 (1868), 308-312,</p> <p>a long time before the classification!</p> <p>The minimal indexes of subgroups of classical simple groups are determined (again pre-classification) in</p> <p>B.N. Cooperstein, "Minimal degree for a permutation representation of a classical group", Israel J. Math. 30 (1978), 213-225.</p> <p>There are apparently a couple of mistakes in Cooperstein's paper, but they concern \$U_n(2)\$ and orthogonal groups over \$F_3\$.</p> <p>In particular, the minimal index of PSL\$(n,q)\$ is \$(q^n-1)/(q-1)\$ except for \$(n,q)\$ = (2,5), (2,7), (2,9), (2,11), or (4,2).</p>