The Generalized Pell Sequences in Groups

Abstract

In this paper, we study the generalized Pell \(p\)-sequences modulo \(m\). Additionally, we define the generalized Pell \(p\)-sequences and the basic generalized Pell sequences in groups, and then examine these sequences in finite groups. Furthermore, we obtain the periods of the generalized Pell \(p\)-sequences and the basic periods of the basic generalized Pell sequences in the binary polyhedral groups \(\langle n,2,2\rangle\), \(\langle2,n,2\rangle\), and \(\langle2,2,n\rangle\).