NON-INNER AUTOMORPHISMS OF ORDER p IN FINITE p-GROUPS OF COCLASS 4 AND 5.

A long-standing conjecture asserts that every finite nonabelian p-group has a non-inner automorphism of order p. This paper proves the conjecture for finite p-groups of coclass 4 and 5 (p ≥ 5). We also prove the conjecture for an odd order nonabelian p-group G with cyclic center satisfying CG(Gpγ3(G)) ∩ Z3(G) ≤ Z(Φ(G)). [ABSTRACT FROM AUTHOR]