proof of Frattini argument

Let gG be any element. Since H is normal, gSg-1H. Since S is a Sylow subgroup of H, gSg-1=hSh-1 for some hH, by Sylow’s theorems. Thus n=h-1g normalizes S, and so g=hn for hH and nNG(S).

Title proof of Frattini argument
Canonical name ProofOfFrattiniArgument
Date of creation 2013-03-22 13:16:05
Last modified on 2013-03-22 13:16:05
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 4
Author bwebste (988)
Entry type Proof
Classification msc 20D20