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The reduction of the `master system' of free motion on the cotangent bundle$T^*G$ of a compact, connected and simply connected, semisimple Lie group isconsidered using the conjugation action of $G$. It is proved that therestriction of the reduced system to the smooth component of the quotient space$T^*G/G$, given by the principal orbit type, inherits the degenerateintegrability of the master system. The proof can be generalized easily toother interesting examples of Hamiltonian reduction.

Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of compact Lie groups