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періодичних видань НАН України
On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations
Репозиторій DSpace/Manakin
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On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations
Інший ID:
2010 MSC:20M20, 05C25.
Посилання:
On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations / P. Catarino, P.M. Higgins, I. Levi// Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 162-171. — Бібліогр.: 18 назв. — англ.
Підтримка:
The first author acknowledges support by the Portuguese Govern-ment through the Portuguese Foundation FCT under the project PEst-OE/MAT/UI4080/2014.
Дата:
2015
Переглядів:
537
Завантажень:
153
Анотація:
It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transformations on a finite chain Xn is a semilattice of idempotents, and so the semigroup of all order-preserving transformations of Xn is not covered by its inverse subsemigroups. This result is used to show that the semigroup of all orientation-preserving transformations and the semigroup of all orientation-preserving or orientation-reversing transformations of the chain Xn are covered by their inverse subsemigroups precisely when n≤3.
