On generalized Clifford groups. I

It is shown that using the basis elements of the generalized Clifford algebra C^m_n we can construct a group G?^m_n called the generalized Clifford group (G.C.G.) which is a generalization of the Dirac group of the 16 Dirac matrices and their negative counterparts. We have studied the irreducible representations of G.C.G. and we have found the connection with the group of linear transformations leaving invariant the expression $\text{∑}\text{i=1}\text{n}\text{(x}{}^{\mathrm{i}}\text{)}{}^{\mathrm{m}}$ for m>2.