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Unformatted text preview:  H : H P  =  HP : P  . Also  G : P  =  G : HP  HP : P  and  G : P  is not divisible by p , because P is a Sylow psubgroup of G . It follows that  H : H P  is not divisible by p , which establishes that H P is a Sylow psubgroup of H . Also it is a normal subgroup of H (for example, by the second isomorphism theorem). By Sylows theorems, we conclude that H P is the unique Sylow psubgroup of G ....
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This note was uploaded on 01/02/2012 for the course MATH 5125 taught by Professor Palinnell during the Fall '07 term at Virginia Tech.
 Fall '07
 PALinnell
 Math, Algebra

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