Quasi-idempotent ranks of some permutation groups and transformation semigroups


BUGAY L.

TURKISH JOURNAL OF MATHEMATICS, cilt.43, ss.2390-2395, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 43 Konu: 5
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1901-52
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.2390-2395

Özet

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.