THE COMPLEX-TYPE FIBONACCI p-SEQUENCES IN FINITE GROUPS

In this paper, we study the complex-type Fibonacci -sequence according to modulo and obtain the periods and the ranks of the complex-type Fibonacci -sequence. Then, we consider the generating matrix of the complex-type Fibonacci -sequence when read modulo and we obtain the cyclic groups. Furthermore, we derive the relationships between the periods of the complex-type Fibonacci -sequence modulo and the orders of the cyclic groups produced. Also, we redefine the complex-type Fibonacci -sequence through the elements of the groups and then examine this sequence in the finite groups. Finally, we obtain the periods of the complex-type Fibonacci -sequence in the dihedral group as applications of the results produced.