Automorphism Orbits of the Group of Unitriangular Matrices

2025/10/10 by Emerson de Melo, de Melo, Emerson, Kato, Júlia
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2510.09353

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

Abstract

Let G be a group. The orbits of the natural action of Aut(G) on G are called the automorphism orbits of G, and their number is denoted by ω(G). Let \mathbbF be an infinite field, and let UT_n(\mathbbF) denote the group of unitriangular matrices over \mathbbF. We show that ω(UT_n(\mathbbF)) is finite for n ≤ 5 and infinite for n ≥ 6.

Related

• The automorphism group of the group of unitriangular matrices over a\n field
• Bijections preserving commutators and automorphisms of unitriangular group
• Orbits of automorphism groups of fields
• Finite groups with only small automorphism orbits
• Finite groups with a large automorphism orbit