For the non-Abelian simple groups with Abelian Sylow 2-subgroups J. H. Walterhas proved the following famous theorem. Lemma 1. If F is a non-Ablian simple group with Abelian Sylow 2-subgroups, thenone of the following...For the non-Abelian simple groups with Abelian Sylow 2-subgroups J. H. Walterhas proved the following famous theorem. Lemma 1. If F is a non-Ablian simple group with Abelian Sylow 2-subgroups, thenone of the following holds:（i）F≌PSL（2,Q）,q】3,q≡3,5（mod 8） or q=2<sup>n</sup>,n≥2;（ii）F≌J<sub>1</sub>;（iii）F≌R（q）,q=3<sup>2m+1</sup>,m≥1.Let G be a finite group and let π<sub>e</sub>（G） denote the set of all orders of elements展开更多
文摘For the non-Abelian simple groups with Abelian Sylow 2-subgroups J. H. Walterhas proved the following famous theorem. Lemma 1. If F is a non-Ablian simple group with Abelian Sylow 2-subgroups, thenone of the following holds:（i）F≌PSL（2,Q）,q】3,q≡3,5（mod 8） or q=2<sup>n</sup>,n≥2;（ii）F≌J<sub>1</sub>;（iii）F≌R（q）,q=3<sup>2m+1</sup>,m≥1.Let G be a finite group and let π<sub>e</sub>（G） denote the set of all orders of elements
