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In this paper, we study matricial representations of certain finitely presented groups with N-generators of order-2. As an application, we consider a group algebra under our representations. Specifically, we characterize the inverses of all group elements in terms of matrices in the group algebra. From the study of this characterization, we realize there are close relations between the trace of the radial operator and the Lucas numbers appearing in the Lucas triangle.

Matricial Representations of Certain Finitely Presented Groups Generated by Order-2 Generators and Their Applications