A high-pressure compressor (12), in particular in a gas turbine (10), has a compressor rotor (17) which is surrounded by a stator (18, 19) thereby forming a main flow channel (25) and which is delimited at the compressor outlet by an end face (30) substantially extending in the radial direction, along which end face cooling air (21) is conveyed in the radial direction for the purpose of cooling. A prolonged service life is achieved in that the end face (30) is provided with a first system (23, 24) for improving the heat transfer between the cooling air (21) and the end face (30).