  We study the possibility of long-range ordering (LRO) in a 3D system of
vertically stacked layers of Ising antiferromagnet on a kagome lattice (SIAKL).
Monte Carlo simulations are carried out for a varying interlayer coupling
strength and a finite-size scaling analysis is performed for selected cases.
Unlike in the related Ising system on a triangular lattice, in which even a
finite number of the layers can stabilize LRO, or the Heisenberg system on the
same kagome lattice, in which LRO emerged in 3D for a sufficient strength of
the interlayer coupling, no LRO could be observed in the present model. This
makes SIAKL a rare example of a 3D Ising paramagnet composed of frustrated
layers coupled by unfrustrated interaction.
