Holonomy groups of four-dimensional pseudo-Riemann spaces

Four-dimensional pseudo-Riemann spaces $\mathcal{V}^4$ with a metric having the signature $(3, 1)$ are investigated. Subgroups of the Lorentz group are described which can be holonomy groups of the pseudo-Riemann spaces $\mathcal{V}^4$: a) with zero Ricci curvature and b) symmetric. The reducibility of the above class of spaces is determined as a function of the holonomy group.