THE RECURRENCE SEQUENCES VIA THE ADJACENCY MATRIX OF THE DIHEDRAL GROUP.

This work develops properties of the recurrence sequences defined by using the characteristic polynomial of the adjacency matrix of the Cayley diagram of the dihedral group. The study of this sequence modulo m yields cyclic groups and semigroups from generating matrix. Also, we extend the sequences defined to groups and then we examine these sequences in finite groups. Finally, we obtain the periods of the extended sequences in the dihedral group D2n as applications of the results obtained. [ABSTRACT FROM AUTHOR]