please help me with this sirs/ma'ams, i can't prove it...
THE COMMUTATOR SUBGROUP OF A FINITE 2-GENERATED P-GROUP OF (NILPOTENCY) CLASS 2 IS CYCLIC
i'm having difficulties on showing that the commutator subgroup is cyclic, please help me.. thanks
maybe someone know the following theorem and knows how to prove or any book, where I can find it:
Let G be a p-group. The indices of centralizers are bounded by p for every x in G. Then, the order of the commutator subgroup is bounded by p:
|G| = p^n, |G:C_G(x)| <= p for all x in G => |G'| <= p