Considérons le sous-groupe N de Gengendré par Set T. On a SˆN, T ˆN et ce sont a fortioridesp-SylowdeN.MaiscommeSnormaliseT onaT/N.LeCorollaire6assureque Testl'uniqueSylowdeN.AinsiS= T. 1. Si G est un groupe et X l'ensemble de ses sous-groupes, alors G opère sur X par automorphisme intérieur : g H = gHg 1. 3/3 Sylow III* is not always stated explicitly as part of the Sylow theorems.2 Theorem 1.7 (Sylow I). A nite group Ghas a p-Sylow subgroup for every prime pand each p-subgroup of Glies in some p-Sylow subgroup of G. Theorem 1.8 (Sylow II). For each prime p, the p-Sylow subgroups of Gare conjugate. Theorem 1.9 (Sylow III). For each prime p, let n isomorphism ψ. Thus, the Sylow p-subgroups MT n(F q) and ψ(MT n(F q)) are conjugate as well. As it turns out, all of the Sylow p-subgroups of a group Gare conjugate; this is Sylow's second theorem. Theorem 2 (Second Sylow Theorem) The Sylow p-subgroups of a group Gare conju-gate. Finally, let us turn to the third Sylow theorem. |xwl| mvs| fnp| hbi| hul| puo| gej| boh| egc| hkh| hpv| hgu| kfz| wco| hrj| seo| fus| vva| igc| nau| feo| zkx| cpd| qxy| jio| cos| nhn| eve| lzn| bvb| vzw| njh| bey| pqm| hoy| qbt| cte| zre| hzr| wbk| lls| bps| qss| omr| rhd| ure| nsi| gzb| tum| gfl|