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We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a finite set S of invertible substitutions such that any invertible substitution can be written as I w • σ 1 • σ 2 • · · · • σ k , where I w is the inner automorphism associated with w, and σ j ∈ S for 1 ≤ j ≤ k. As a consequence, M is the matrix of an(More)