Defining relations of semigroups of all directed transformations of an ordered finite set

E. S. Lyapin

A. I. Herzen Leningrad State Pedagogical University

Abstract: The semigroup $\mathfrak A$ of all transformations $X$ of a finite (partially) ordered set $\Omega$, such that $\alpha\le X\alpha$ for all $\alpha\in\Omega$, is considered. All possible generating sets of a $\Omega$ are elucidated. Only one of those sets is irreducible. A system of defining relations is found for that generating set.

UDC: 512.2

Received: 24.07.1967

 English version: Mathematical Notes, 1968, 3:6, 419–422

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