2023/10/12 by Alan J. Cain, Cain, Alan J., António Malheiro +3
Computer Science · #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2310.08481
Cameron, et al. determined the maximum size of a null subsemigroup of the full transformation semigroup T(X) on a finite set X and provided a description of the null semigroups that achieve that size. In this paper we extend the results on null semigroups (which are commutative) to commutative nilpotent semigroups. Using a mixture of algebraic and combinatorial techniques, we show that, when X is finite, the maximum order of a commutative nilpotent subsemigroup of T(X) is equal to the maximum order of a null subsemigroup of T(X) and we prove that the largest commutative nilpotent subsemigroups of T(X) are the null semigroups previoulsy characterized by Cameron, et al..