Complex sentence: Tensor products and the inverses of linearized invertible sheaves are again linearized in the natural way and thus linearized line bundles on a scheme "X" form a subgroup of the Picard group of "X".
Split into simpler sentences: Tensor products and the inverses of linearized invertible sheaves are again linearized in the natural way. Thus, the linearized line bundles on a scheme "X" form a subgroup of the Picard group of "X".