On certain subsemigroups of finite oriented and order-decreasing full transformations
Abstract
Let ORDn be the semigroup consisting of all oriented and order-decreasing full transformations on the finite chain Xn=\ 1<·s<n \, and for 1≤ r≤ n-1, let ORD(n,r) =\α ∈ ORDn\, :\, im(α ) ≤ r\. In this paper, we determine the cardinality of ORD(n,r) and the number of nilpotent elements of ORD(n,r), we find a minimal generating set and the rank of ORD(n,r), and moreover, we characterize all maximal subsemigroups of ORD(n,r) for each 3≤ r≤ n-1.
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