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Algebra and Discrete Mathematics, 2006, Issue 4, Pages 126–140
(Mi adm284)
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This article is cited in 1 scientific paper (total 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.
Received: 12.12.2004 Revised: 29.03.2007
Citation:
A. Stronska, “Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree”, Algebra Discrete Math., 2006, no. 4, 126–140
Linking options:
https://www.mathnet.ru/eng/adm284 https://www.mathnet.ru/eng/adm/y2006/i4/p126
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