Properties of the supercooled amorphous state have been studied for the Gaussian core model at reduced density ρ*=1. By monitoring the self-diffusion constant and mean energy during a slow cooling to absolute zero, a glass transition was observed separating supercooled fluid from a rigid amorphous packing. At this glass transition the Wendt–Abraham criterion for the pair correlation function (g(2)min/g(2)max=0.14) is satisfied. However, former suggestions that second-peak splitting in g(2) universally signifies the glassy state for monatomic substances are not supported.