Patali Komma - Ms. Komma Patali Ph.D. Candidate School of Mathematics, IISER Thiruvananthapuram, Thiruvaanthapuram, India

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 ۴ and ۵ (p\ge ۵). We also prove the conjecture for an odd order nonabelian p-group G with cyclic center satisfying C_G(G^p\gamma_۳(G))\cap Z_۳(G)\le Z(\Phi(G)).

finite p-groups, Non-inner automorphisms, Coclass