The study investigates the hypothesis that fast neuronal oscillations (gamma, 20–80 Hz) in the neocortex and hippocampus can emerge from a random network of interconnected GABAergic fast-spiking interneurons. Key conditions for population synchronization are identified, including: (1) spike afterhyperpolarization amplitude must be above the GABA$_A$ synaptic reversal potential; (2) the ratio of synaptic decay time constant to oscillation period should be sufficiently large; (3) heterogeneities should be modest due to a steep frequency–current relationship of fast-spiking neurons; and (4) a critical (minimal) average number of synaptic contacts per cell is required for large-scale network synchronization, which is not sensitive to network size. The study demonstrates that GABA$_A$ synaptic transmission provides a suitable mechanism for synchronized gamma oscillations in a sparsely connected network of fast-spiking interneurons, potentially maintaining subthreshold oscillations in principal cell populations and synchronizing discharges of spatially distributed neurons.The study investigates the hypothesis that fast neuronal oscillations (gamma, 20–80 Hz) in the neocortex and hippocampus can emerge from a random network of interconnected GABAergic fast-spiking interneurons. Key conditions for population synchronization are identified, including: (1) spike afterhyperpolarization amplitude must be above the GABA$_A$ synaptic reversal potential; (2) the ratio of synaptic decay time constant to oscillation period should be sufficiently large; (3) heterogeneities should be modest due to a steep frequency–current relationship of fast-spiking neurons; and (4) a critical (minimal) average number of synaptic contacts per cell is required for large-scale network synchronization, which is not sensitive to network size. The study demonstrates that GABA$_A$ synaptic transmission provides a suitable mechanism for synchronized gamma oscillations in a sparsely connected network of fast-spiking interneurons, potentially maintaining subthreshold oscillations in principal cell populations and synchronizing discharges of spatially distributed neurons.