Quasi-idempotent ranks of some permutation groups and transformation semigroups


BUGAY L.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.5, pp.2390-2395, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 5
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1901-52
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.2390-2395

Abstract

Let S-n, A(n), I-n, T-n, and P-n be the symmetric group, alternating group, symmetric inverse semigroup, (full) transformations semigroup, and partial transformations semigroup on X-n = {1, ... , n} , for n >= 2, respectively. A non-idempotent element whose square is an idempotent in P-n is called a quasi-idempotent. In this paper first we show that the quasi-idempotent ranks of S-n, (for n >= 4) and A n (for n >= 5) are both 3. Then, by using the quasi-idempotent rank of , we show that the quasi-idempotent ranks of I-n, T-n, and P-n, (for n >= 4) are 4, 4 , and 5, respectively.