Let f(p, n) be the number of pairwise nonisomorphic p-groups of order \(p^n\), and let g(p, n) be the number of groups of order \(p^n\) whose automorphism group is a p-group. We prove that the limit, as p grows to infinity, of the ratio g(p, n) / f(p, n) equals 1/3 for \(n=6,7\).
W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system. I. The user language, Computational algebra and number theory (London, 1993), J. Symbolic Comput. 24 (1997), 235–265.MathSciNetCrossRefMATHGoogle Scholar
P. A. Brooksbank, J. Maglione, andJ. B. Wilson, A fast isomorphism test for groups whose Lie algebra has genus 2, to appear, J. Algebra, arXiv:1508.03033.