Some automorphism groups of finite p-groups

2013/01/01 by Yassine Guerboussa, Guerboussa, Yassine, Miloud Reguiat +1
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1301.0085

openalex publication_date 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A conjecture of Berkovich asserts that every non-simple finite p-group has a non-inner automorphism of order p. This conjecture is far from being proved despite the great effort devoted to it. In this paper we prove it for p-groups of coclass 2, provided that p is odd. Some related results are also proved, and may be considered as interesting independently.

Citations

• On central automorphisms of groups and nilpotent rings
• Powerful p-groups have noninner automorphisms of order p and some cohomology

Related

• On the non-inner automorphism conjecture of finite p-groups
• Non-inner automorphisms of order p in finite p-groups of coclass 4 and coclass 5
• A survey on the Non-inner Automorphism Conjecture
• Non-inner automorphisms of order p in finite p-groups of coclass 3
• A note on non-inner automorphism conjecture