  The C_{\lambda}-extended oscillator algebra is generated by
{1,a,a^{\dagger},N,T}, where T is the generator of the cyclic group C_{\lambda}
of order \lambda. It can be realized as a generalized deformed oscillator
algebra (GDOA). Its unirreps can thus be exhibited using the representation
theory of GDOAs and their carrier space show a Z_{\lambda} grading structure.
Within its infinite-dimensional Fock space representation, this algebra
provides a bosonization of parasupersymmetric quantum mechanics of order p=
\lambda - 1.
