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- W2388559305 abstract "Let G be a group,an automorphism φ: G → G is called a commuting automorphism,if for all x ∈ G,φ(x) x = xφ(x). Let n be a positive integer larger than 3 and F a field. Denote by Tnthe multiplicative group consisting of all n × n invertible upper triangular matrices over F.Prove that a map φ: Tn→ Tnis a commuting automorphism on Tnif and only if there exist group honmomorphisms σi: F*→ F*,1 ≤ i ≤ n,such that φ(A) =(∏ni=1σi(aii)) A,for A =(aij)n × n∈Tn,and for any k = 1,2,…,n and any a ∈ Imσk,the equation xσ1(x) σ2(x) …σn(x) = a has a unique solution in F*." @default.
- W2388559305 created "2016-06-24" @default.
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- W2388559305 date "2015-01-01" @default.
- W2388559305 modified "2023-09-24" @default.
- W2388559305 title "Commuting Automorphisms on Invertible Upper Triangular Matrices" @default.
- W2388559305 hasPublicationYear "2015" @default.
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