Quasi-idempotent ranks of some permutation groups and transformation semigroups

Leyla BUGAY

Makale detayları

Quasi-idempotent ranks of some permutation groups and transformation semigroups

Yazarlar:

Leyla BUGAY

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 5, pp.2390-2395

Belge Tipi:

Makale

Yayın Tarihi:

9/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000745539

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

Let SnSnS_{n}, AnAnA_{n}, InInI_{n}, TnTnT_{n}, and PnPnP_{n} be the symmetric  group, alternating group, symmetric inverse semigroup, (full)  transformations semigroup, and partial transformations semigroup on  Xn={1,…,n}Xn={1,…,n}X_{n}=\{1,\dots ,n\}, for n≥2n≥2n\geq 2, respectively. A  non-idempotent element whose square is an idempotent in PnPnP_{n} is  called a quasi-idempotent. In this paper first we show that the  quasi-idempotent ranks of SnSnS_{n} (for n≥4n≥4n\geq 4) and AnAnA_{n} (for  n≥5n≥5n\geq 5) are both 333. Then, by using the quasi-idempotent rank of  SnSnS_{n}, we show that the quasi-idempotent ranks of InInI_{n}, TnTnT_{n},  and PnPnP_{n} (for n≥4n≥4n\geq 4)  are 444, 444, and 555, respectively.

Makale detayları

Quasi-idempotent ranks of some permutation groups and transformation semigroups

Yazarlar: Leyla BUGAY

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 5, pp.2390-2395

Belge Tipi: Makale

Yayın Tarihi: 9/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000745539

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Leyla BUGAY

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 5, pp.2390-2395

Belge Tipi:

Makale

Yayın Tarihi:

9/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000745539

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098