This article is cited in 1 paper

RESEARCH ARTICLE

Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree

A. Stronska

Kyiv National Taras Shevchenko University, department of algebra and mathematical logics, Glushkova st., 6, Kyiv

Abstract: This paper deals with a semigroup of order-decreasing transformations of a rooted tree. Such are the transformations $\alpha$ of some rooted tree $G$ satisfying following condition: for any $x$ from $G$ $\alpha(x)$ belongs to a simple path from $x$ to the root vertex of $G$. We describe all subsemigroups of the mentioned semigroup, which are maximal among nilpotent subsemigroups of nilpotency class $k$ in our semigroup. In the event when rooted tree is a ray we prove that all these maximal subsemigroups are pairwise nonisomorphic.

Keywords: semigroup, order-decreasing, non-isomorphic.

MSC: 20M20

Received: 12.12.2004
Revised: 29.03.2007

Language: English

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