ON A SPECIAL CLASS OF FINITE p-GROUPS OF MAXIMAL CLASS

Abstract

In this paper, we study the finite p—group G of maximal class in which every nonabelian subgroup H satisfies C_G(H) = Z(H).  We prove here that a finite p—group G of maximal class is metabelian if every nonabelian subgroup H satisfies C_G(H) = Z(H), furthermore, if p ≠ 3, |G| ≥ ¸p^2p, then there is an abelian subgroup of index p in G.