2019/08/04 by Raimundo Bastos, Alex C. Dantas, Alex Carrazedo Dantas +1
Mathematics · #Automorphism #Automorphism group #Finite Group Theory Research #Finite group #Geometric and Algebraic Topology #Inner automorphism #Nilpotent #Order (exchange) #Outer automorphism group #Rank (graph theory) #Rings, Modules, and Algebras #math.GR #msc:20E22 #msc:20E36
paper · pdf · doi:10.1007/s10711-020-00525-7
published as Geometriae Dedicata volume 209, pages119. -- 123 (2020) - The final publication is available at https://link.springer.com/article/10.1007/s10711-020-00525-7 · Submitted to an international journal Geometriae Dedicata (2020)
arxiv created 2019/08/04 · openalex created_date 2019/08/13 · openalex publication_date 2020/03/17 · arxiv updated 2020/10/20 · openalex updated_date 2026/08/05
Let G be a group. The orbits of the natural action of Aut(G) on G are called ``automorphism orbits'' of G, and the number of automorphism orbits of G is denoted by ω(G). We prove that if G is a soluble group with finite rank such that ω(G)< ∞, then G contains a torsion-free characteristic nilpotent subgroup K such that G = K \rtimes H, where H is a finite group. Moreover, we classify the mixed order soluble groups of finite rank such that ω(G)=3.