Group relationships and homomorphisms of Boolean matrix semigroups

The image matrix obtained from a blocked Boolean matrix gives a homomorphism provided that the product of any two nonzero blocks is nonzero. All maximal nonzero Boolean matrix semigroups are found. Those invariant under conjugations by a permutation matrix have the form G_i = {A: the sum of any ith rows of A (or all rows) has at least i ones (or all ones)}.