A p-group was called
p-automorphic by Boen, if its automorphism group is transitive on elements of order
p. Boen conjectured that if p is odd, then such a p-group is abelian. Let P be a
nonabelian p-automorphic p-group, p odd, generated by n elements. Boen proved
that n > 3, and in joint work with Rothaus and Thompson proved that n > 5.
Kostrikin then showed that n > p + 6, as a corollary of results on homogeneous
algebras. In this paper it is shown that n > 2p + 3, using Kostrikin’s methods, and
his proof is somewhat simplified by eliminating special case considerations for small
values of p.
