Conjugacy classes of the order-preserving and order-decreasing partial one-to-one transformation semigroups
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Date
2019-03
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of Science, Technology, Mathematics and Education. Published by the Department of Science Education, Federal University of Technology, Minna, Nigeria.
Abstract
In this paper I_n is considered to be the partial one-to-one transformation semigroup on . The order-preserving and order-decreasing partial one-to-one transformation semigroup(〖IC〗_n) is defined to be the subsemigroups of I_n. The nilpotent and idempotent elements of 〖IC〗_n were then obtained from its conjugacy classes using path structure to be n+1 and 1/192 n^4-1/16 n^3+29/48 n^2-n+2 respectively. The index and period of each conjugacy classes were also found. More so, some properties of conjugacy classes were stated.
Description
Keywords
Semigroup,, Order-preserving, Nilpotent, Idempotent Elements., Transformation Semigroup,, Path Structure,, Conjugacy,, Order-decreasing, Partial one-to-one
Citation
Ugbene, I. J., Bakare, G. N., and Ibrahim G. R. (2019): Conjugacy classes of the order-preserving and order-decreasing partial one-to-one transformation semigroups. Journal of Science, Technology, Mathematics and Education.