Quasigroups connected with Clifford groups

In Clifford groups, a nonassociative product is defined which leads to the definition of nonassociative groups. These nonassociative groups have matri x representations on the condition that the "row by column" product of two matrices is replaced by the "column by column" product. A nonassociative gr oup of transformations connected with the Lorentz group is determined, toge ther with its irreducible, double-valued matrix representation, whose matri ces undergo the "column by column" product.