A focal subgroup theorem for outer commutator words
Cristina Acciarri · IRIS UNIMORE (University of Modena and Reggio Emilia) · 2012
Let G be a finite group of order p a m, where p is a prime and m is not divisible by p, and let P be a Sylow p-subgroup of G.If w is an outer commutator word, we prove that P ∩ w(G) is generated by the intersection of P with the set of mth powers of all values of w in G.