Resumen
A set of direct and inverse elements are examined and compared with a four-dimensional orthonormal basis. The aggregate of even substitutions of fourth power as a product of two transpositions are formed on this finite set. The finite set of substitutions is represented by monomial (1, 0, ?1)-matrices of fourth order. An isomorphism of quaternion group and two noncommutative subgroups of eighth order is determined. Properties of four aggregates of basic matrices, corresponding to quaternion matrices, are examined.