Finite p-groups with small automorphism group

2014/06/22 by Jon González‐Sánchez, Gonzalez-Sanchez, Jon, Andrei Jaikin‐Zapirain +1
Mathematics · #20D15 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1406.5772

openalex publication_date 2014/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each prime p we construct a family \G_i\ of finite p-groups such that |\Aut (G_i)|/|G_i| goes to 0, as i goes to infinity. This disproves a well-known conjecture that |G| divides |\Aut(G)| for every non-abelian finite p-group G.

Related

• A note on automorphisms of finite p-groups
• On automorphisms of finite p-groups
• Automorphism Groups of Finite p-Groups: Structure and Applications
• On the isomorphism problem for certain p-groups
• Automorphisms of small prime power groups