The Generalized Order-k Lucas Sequences in Finite Groups

Abstract EN

We study the generalized order-k Lucas sequences modulo m.

Also, we define the ith generalized order-k Lucas orbit lAi,{α1,α2,…,αk-1}(G) with respect to the generating set A and the constants α1,α2, and αk-1 for a finite group G=〈A〉.

Then, we obtain the lengths of the periods of the ith generalized order-k Lucas orbits of the binary polyhedral groups 〈n,2,2〉,〈2,n,2〉,〈2,2,n〉 and the polyhedral groups (n,2,2), (2,n,2), (2,2,n) for 1≤i≤k.