What question did this study set out to answer?

The study aims to determine when the automorphism group of the wreath product of two structures corresponds to the wreath product of their automorphism groups.

June 4, 2026

Automorphism Group of a Wreath Product of Binary Structures

Key Points

The study aims to determine when the automorphism group of the wreath product of two structures corresponds to the wreath product of their automorphism groups.
Generalization of previous results to binary structures
Utilization of modular decomposition
Completion of previous analyses regarding automorphism groups and wreath products
Inclusion of the previously ignored case in the study of automorphism groups

Abstract

ABSTRACT 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.

Automorphism Group of a Wreath Product of Binary Structures

Key Points

Abstract

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