The Complex-type Pell p-Numbers in Finite Groups

Abstract

In this paper, we study the complex-type Pell p-numbers modulo m and then we obtain the periods and the ranks of the complex type Pell p-numbers modulo m. Also, we give some results on the periods and the ranks of the complex-type Pell p-numbers modulo m. Then, we consider the multiplicative orders of the complex-type Pell p-matrix when read modulo m. Also, we give the relationships between the periods of the complex-type Pell p-numbers modulo m and the orders of the cyclic groups produced. We redefine the complex-type Pell p-numbers by means of the elements of groups. Finally, we obtain the periods of the complex-type Pell 2-numbers in the semidihedral group SD_2^m , (m ≥ 4) as applications of the results.