Algebraic Theories of AUNU Permutation Using Group Action with Non- Prime Order

Permutation groups have played important roles in method of enumerating combinatorial objects in recent times. However, the study of the applicability AUNU permutation groups using group action is challenging. In this paper, a new method of constructing group action using the subsequences of (123)- avoiding of AUNU Permutation patterns is provided. The method used the generating function of AUNU groups in the construction to obtain some geometric structures of orbits resembling to lattice. The research further established some algebraic properties of group action as well as orbit and stabilizer in permutation groups which are relevant to the study of finite group structures. The paper also providedsome motivations for the study of group action in an abstract domain.