We examine the automorphism group of the wreath product of binary structures, completing previous work on the topic.
We consider the question of when the automorphism group of the wreath (lexicographic) product of two structures is the wreath product of the automorphism groups of the two structures. Sabidussi gave partial soluLet us formalize our presentationtions, others (Hemminger, Hahn, Dobson and Morris) continued the work. All the previous work ignored one particular case and here we complete the study by generalizing to binary structures using modular decomposition.
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Hahn et al. (2026) studied this question.
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