On automorphisms of finite p-groups

2018/03/21 by Hemant Kalra, Kalra, Hemant, Deepak Gumber +1
Engineering · Mathematics · #20D15 #20D45 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1803.07853

openalex publication_date 2018/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved in [J. Group Theory, \bf 10 (2007), 859-866] that if G is a finite p-group such that (G,Z(G)) is a Camina pair, then |G| divides |\Aut(G)|. We give a very short and elementary proof of this result.

Related

• A note on automorphisms of finite p-groups
• Finite p-groups with small automorphism group
• Camina pairs that are not p-closed
• Equality of certain automorphism groups of finite p-groups
• Class-Preserving Automorphisms of a Family of Finite p-Groups