Section InnerAutCyclicPgroup.
Variables (gT : finGroupType) (p : nat) (G C : {group gT}).
Hypothesis nCG : G \subset 'N(C).

Lemma logn_quotient_cent_cyclic_pgroup :
p.-group C -> cyclic C -> logn p #|G / 'C_G(C)| <= (logn p #|C|).-1.