TURKISH JOURNAL OF MATHEMATICS, cilt.43, sa.5, ss.2390-2395, 2019 (SCI-Expanded)
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.