# Some Geometric Characterization Of Star-like 3D Conjugacy C3ω∗n On Partial One-One Transformation Semigroups

### Abstract

Let Xn = {1, 2, 3, ...} be a set of distinct non negative integer then C3ω∗n be star-like conjugacy transformation semigroup for all D(α∗) (domain of α∗) and I(α∗) (Image of α∗) such that an operator | αωi − ωi+1 |≤| αωi − ωi | was generated. A star-like transformation semigroup is said to satisfy collapse function if C+(α∗) =| ∪tα− : t ∈ Tαω∗n | while the finding shows that the collapse of 3D star-like conjugacy classes are zero. The geometry model of 3D starlike conjugacy was obtained by using folding principle on a standard A4 paper which shows the star-like 3D conjugacy relation α(ij) = αi+αi+1 αi−αi+1 = αi+1+αi αi+1−αi .Some tables were formed to analyse the structure of star-like derank of C3ω∗n be | n − Imα∗ |= d, star-like collapse C+(α∗) =| ∪tα−1 : t ∈ Tαω∗n |, Star-like relapse C−(α∗) =| n−C+(α∗), Star-like pivot of C3ω∗n be |n.r+(α∗)c−(α∗) + c+(α∗|= p and Star-like joint of C3ω∗n be | r+(α∗)−m∗(α∗)−C+(α∗)+n |= j . The study conclude that C3ω∗n has n order conjugacy classes and we show that ϕ ∈ C3ω∗n.

*International Journal of Mathematical Sciences and Optimization: Theory and Applications*,

*10*(3), 57 - 66. Retrieved from http://ijmso.unilag.edu.ng/article/view/2196

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