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1. While the present paper is concerned chiefly with continuous groups, its results may be readily utilized for discontinuous groups.* Indeed, the finite form of the general transformation of the group is known ah initio. Further, the method is applicable to the construction of a linear Cm> q -ary group isomorphic to an arbitrary m-ary linear group. 2. The formula of composition of m-ary linear homogeneous substitutions

Concerning a linear homogeneous group in 𝐶_{𝑚,𝑞} variables isomorphic to the general linear homogeneous group in 𝑚 variables