Timeline for A group 2-transitive
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2012 at 9:14 | comment | added | Derek Holt | If $G$ has $p+1$ Sylow $p$-subgroups, then its action by conjugation on the set of Sylow $p$-subgroups is 2-transitive, and the point stabilizer has order $p(p-1)/2$ with a normal subgroup of order $p$. A group with those properties is isomorphic to ${\rm PSL}(2,p)$ - you don't even need the classification of fintie simple groups for that - it follows from the result proved in: Hering, Christoph; Kantor, William M.; Seitz, Gary M. Finite groups with a split BN-pair of rank 1. I. J. Algebra 20 (1972), 435–475. | |
| Apr 22, 2012 at 13:00 | comment | added | R K | Thank you for you answer. Yes $p$ is prime. Also let the number of Sylow $p$-subgroup $G$ equal to the number of Sylow $p$-subgroup $PSL(2,p)$. Now: whether $G$ isomorphic to $PSL(2,p)$? | |
| Apr 22, 2012 at 11:09 | comment | added | Derek Holt | I have been assuming that $p$ is prime. Is that right? | |
| Apr 21, 2012 at 18:37 | answer | added | Derek Holt | timeline score: 8 | |
| Apr 21, 2012 at 15:19 | history | edited | R K | CC BY-SA 3.0 |
deleted 7 characters in body
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| Apr 21, 2012 at 13:45 | history | asked | R K | CC BY-SA 3.0 |