Let G be a group of order p
am where p is a prime not dividing m. Show the following
1. Sylow p-subgroups of G exist; i.e. Sylp(G) 6= ?.2. If P ? Sylp(G) and Q is any p-subgroup of G, then there exists g? G such that Q 6gP g?1
; i.e. Q is contained in some conjugate of P. In particular, anytwo Sylow p-subgroups of G are conjugate in G.
3. np ? 1 (mod p) and np|m.
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
(Save $1 )
One time Pay
(Save $5 )
Billed Monthly
*First month only
You can see the logs in the Dashboard.
