This thesis focuses on Salingaros Vee groups and Clifford algebras. Salingaros defined families N2k--1, N2k, O2k and Sk of finite 2-groups related to Clifford algebras Cℓp,q. In 2001, Chernov observed that Clifford algebras can be obtained as a homomorphic image of a group algebra R[G] where G is a finite 2-group with generators fulfilling certain relations. One can prove that every Clifford algebra Cℓp,q is isomorphic to a quotient of the group algebra R[Gp,q], where Gp,q is the Salingaros Vee group, modulo an ideal J = (1 + tau) generated by 1 + tau for a central element tau of order 2. Thus, Clifford algebras can be classified as images of group algebras R[Gp,q]. Since the Clifford algebras Cℓp,q and the group algebras R[ Gp,q] are Z2-graded and the ideal J is homogeneous, the quotient algebra R[G p,q]/J Z2-graded. In some instances, the R-algebra isomorphism R[ Gp,q]/J and Cℓp,q for a suitable maximal normal subgroup H of G p,q. The author conjectures that each Clifford algebra Cℓp,q is graded-isomorphic with R[ Gp,q]/J for a suitable choice of a maximal subgroup H in Gp,q..