Automorphisms of small prime power groups

2015/05/14 by Joshua Maglione, Maglione, Joshua
Computer Science · Mathematics · #Advanced Topics in Algebra #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1505.03881

openalex publication_date 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If f(p, n) is the number of pairwise nonisomorphic groups of order pⁿ, and g(p,n) is the number of groups of order pⁿ whose automorphism group is a p-group, then, for n ≤ 7, we prove that the ratio g(p,n)/f (p,n) is bounded away from 1 as the prime p grows to infinity. In addition, we provide some data on the number of groups whose automorphism group is a group of prime power order, for primes no larger than 11.

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