Theorems you should know UW-MadisonGuillermo Mantilla(A) (Isaacs,5.11) Let G be a nite group and write np(G) = jSylp(G)j.Then npdivides jGj and np(G) 1 mod p.In fact,np(G) 1 mod peif pe jS:STj for all S;T 2 Sylp(G) with S 6= T.(A.1) Suppose that G is a nite...