The Cyclic Groups via Bezout Matrices

Abstract

<p>In this paper, we define the Bezout matrices by the aid of the characteristic polynomials of the <em>k</em>-step Fibonacci, the generalized order-<em>k</em> Pell and the generalized order-<em>k</em> Jacobsthal sequences then we consider the multiplicative orders of the Bezout matrices when read modulo <em>m</em>. Consequently, we obtain the rules for the order of the cyclic groups by reducing the Bezout matrices modulo <em>m</em>.</p>