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Turkish Journal of Mathematics

Abstract

For n ≥ 2, let Pn , In , Tn , and Sn be the partial transformation semigroup, symmetric inverse semigroup, (full) transformation semigroup, and symmetric group on the set Xn = {1, . . . , n}, respectively. In this paper, we find the ranks of certain subsemigroups of Pn , In , and Tn consisting of transformations with idempotent complement whose restrictions to the set Xm belong to the (possible) semigroup Sm, Im, Tm, or Pm for 1 ≤ m ≤ n − 1.

DOI

10.55730/1300-0098.3516

Keywords

idempotent, Partial (full) transformation semigroup, rank, symmetric group, symmetric inverse semigroup

First Page

414

Last Page

422

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