Tropical matrices with cyclic centralizer groups

Key Points

• The aim is to investigate the structure of n-order tropical matrices and their centralizer groups through group theory.
• Described the structure of centralizer groups for n-order tropical matrices as regular permutation groups.
• Provided necessary and sufficient conditions for centralizer groups to be n-order cyclic groups under isomorphism.
• Examined the correspondence between centralizer groups and 2-closed permutation groups.
• Outlined the structural properties of n-order tropical matrices and their centralizer groups.
• Identified conditions transforming the well-known multicycle conjecture into a study of tropical matrix structures with non-trivial centralizer groups.
• Demonstrated the significance of structural connections within permutation groups.