Abstract
AbstractCameron et al. determined the maximum size of a null subsemigroup of the full transformation semigroup $$\mathcal {T}(X)$$
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 $$\mathcal {T}(X)$$
T
(
X
)
is equal to the maximum order of a null subsemigroup of $$\mathcal {T}(X)$$
T
(
X
)
and we prove that the largest commutative nilpotent subsemigroups of $$\mathcal {T}(X)$$
T
(
X
)
are the null semigroups previously characterized by Cameron et al.
Funder
Universidade Nova de Lisboa
Publisher
Springer Science and Business Media LLC
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