Semigroups of Transformations Commuting with Injective Nilpotents
Janusz Konieczny · Communications in Algebra · 2004
For an injective nilpotent η in the semigroup P T n of partial transformations on a set with n elements, let C(η) be the semigroup of all elements of P T n commuting with η. The structure of C(η) in terms of Green's relations is determined (including the partial orders of ℒ-, ℛ-, and 𝒥-classes), the regular elements of C(η) are characterized, and a formula for the order of C(η) is given.