On The Jacobsthal-Padovan p-Sequences in Groups

Abstract

Abstract In [5], Deveci defined the Jacobsthal-Padovan p-sequence. In this paper,we extend this sequence to groups. Then we define the Jacobsthal-Padovan p-orbit and we study the Jacobsthal-Padovan p-orbits of the finite groups in detail. Furthermore, we obtain the lengths of the periods of the Jacobsthal-Padovan p-orbits of the Fox groups G1,l for l ≥ 3 as applications of the results.