  C$_{\lambda}$-extended oscillator algebras, where C$_{\lambda}$ is the cyclic
group of order $\lambda$, are introduced and realized as generalized deformed
oscillator algebras. For $\lambda=2$, they reduce to the well-known
Calogero-Vasiliev algebra. For higher $\lambda$ values, they are shown to
provide in their bosonic Fock space representation some interesting
applications to supersymmetric quantum mechanics and some variants thereof: an
algebraic realization of supersymmetric quantum mechanics for cyclic shape
invariant potentials of period $\lambda$, a bosonization of parasupersymmetric
quantum mechanics of order $p = \lambda-1$, and, for $\lambda=3$, a
bosonization of pseudosupersymmetric quantum mechanics and orthosupersymmetric
quantum mechanics of order two.
