Graphical Representation of Conjugacy Classes in the Order ? Preserving Partial One ? One Transformation Semigroup

Mogbonju M. M., Ojo O. A., Ogunleke I.A.

Abstract: Let X_n={1, 2, 3,. . , n} be the finite set of n objects. The set of all partial transformation of n objects forms a semigroup under the usual composition of functions. It is denoted by T_n, when it is full or total. , I_n, when it is partial one - one and P _n when it is strictly partial. The elements of conjugacy classes of partial one one transformation were studied. The elements in each conjugacy were represented using two line notation. Finally the elements were arranged in their respective conjugacy class with the aids of unlabelled graph. The elements with the same graph structures will contained in the same conjugacy class.

Keywords: Semigroup, transformation semigroup, conjugacy, conjugacy classes, graph, order preserving partial one one transformation semigroup

How to Cite?: Mogbonju M. M., Ojo O. A., Ogunleke I.A., "Graphical Representation of Conjugacy Classes in the Order ? Preserving Partial One ? One Transformation Semigroup", Volume 3 Issue 12, December 2014, International Journal of Science and Research (IJSR), Pages: 711-721, https://www.ijsr.net/getabstract.php?paperid=OCT14858, DOI: https://dx.doi.org/10.21275/OCT14858

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