Let G be a group of order 315 and suppose that G has a normal
3-Sylow subgroup. Prove that G has a normal 5-Sylow subgroup and a
normal 7-Sylow subgroup.
Hint: Determine the p-Sylow subgroups of G/P3, where P3 is the
normal 3-Sylow subgroup of
G.
Let G Be A Group Of Order 315 And Suppose That G Has A Normal 3 Sylow Subgroup Prove That G Has A Normal 5 Sylow Subgro 1 (12.63 KiB) Viewed 35 times
Let G be a group of order 315 and suppose that G has a normal 3-Sylow subgroup. Prove that G has a normal 5-Sylow subgroup and a normal 7-Sylow subgroup. Hint: Determine the p-Sylow subgroups of G/Ps, where Ps is the normal 3-Sylow subgroup of G.
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