Vol. 26, No. 3, 1968

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ISSN: 0030-8730
p-automorphic p-groups and homogeneous algebras

Larry Lee Dornhoff

Vol. 26 (1968), No. 3, 447–453
Abstract

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.

Mathematical Subject Classification
Primary: 20.22
Milestones
Received: 28 August 1967
Published: 1 September 1968
Authors
Larry Lee Dornhoff