Conditions for the reduction of the time-independent neutron transport equation to an energy-independent (one-group) equation are discussed. It is shown that a meaningful reduction is equivalent to angular flux separability into a product of an energy spectrum and a spatial and angular function. It is proven that such a separability in a finite system is possible if and only if the total cross section is energy independent, provided some auxiliary conditions are met. The physical situations in which these conditions are satisfied and the similarity to the so-called first fundamental theorem of reactor theory are discussed.