It is established that cyclotron resonance (CR) in a high-quality GaAs/AlGaAs two-dimensional electron system (2DES) originates as a textit{pure} resonance, that does not hybridize with dimensional magnetoplasma excitations. The magnetoplasma resonances form a fine structure of the CR. The observed fine structure of the CR results from the interplay between coherent radiative and incoherent collisional mechanisms of 2D plasma relaxation. We show that the range of 2DES filling factors from which the phenomenon arises is intimately connected to the fundamental fine-structure constant.