Apparatus for combustion of a fuel-oxidizer mixture in a combustion chamber of a turbogroup, in particular of a power plant wherein total oxidizer flow is divided into a main oxidizer flow and a secondary oxidizer flow. The main oxidizer flow is lean mixed with a main fuel flow in a premix burner, and the mixture is fully oxidized in the combustion chamber. The secondary oxidizer flow is divided into a pilot oxidizer flow and a heat-exchanging oxidizer flow. The pilot oxidizer flow is rich mixed with a pilot fuel flow, and the mixture is partially oxidized in a catalyst, with hydrogen being formed. Downstream of the catalyst, the partially oxidized pilot fuel-oxidizer mixture and the heat-exchanging oxidizer flow are together introduced into at least one zone which is suitable for stabilizing the combustion of the main fuel-oxidizer mixture.