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 $⟨n,2,2⟩$, $⟨2,n,2⟩$, and $⟨2,2,n⟩$.