On the Addition Modulus of the Aunu Pattern andomega;i and#1013; Gp: An Investigation of Some Topological Properties

This paper investigates the topological properties on the structure generated by the addition modulus of the Aunu permutation pattern 𝑤𝑖. The pattern 𝑤𝑖 has the generating function defined as: 𝜔𝑖=(1 (1+𝑖)𝑚𝑜𝑑𝑝 (1+2𝑖)𝑚𝑜𝑑𝑝 (1+3𝑖)𝑚𝑜𝑑𝑝………(1+((𝑝−1)𝑖)𝑚𝑜𝑑𝑝) For 𝑖=1,2,..𝑝−1. The numbers are arrangement on the structure 𝑋={1,….,𝑃} for primes p ≥ 5. It has been established in this paper that the generated set is a topology on 𝑋, it is not a convex set and finally, not a 𝜎-algebra.