Non-inner automorphisms of order p in finite p-groups of coclass 4 and coclass 5

Abstract

A long-standing conjecture asserts that every finite nonabelian p-group has a non-inner automorphism of order p. In this paper we prove the conjecture for finite p-groups of coclass 4 and coclass 5 (p ≥ 5). We also prove the conjecture for an odd order nonabelian p-group G with cyclic center satisfying