  Albuquerque and Majid have shown how to view Clifford algebras $\cl_{p,q}$ as
twisted group rings whereas Chernov has observed that Clifford algebras can be
viewed as images of group algebras of certain 2-groups modulo an ideal
generated by a nontrivial central idempotent. Ablamowicz and Fauser have
introduced a special transposition anti-automorphism of $\cl_{p,q}$, which they
called a "transposition", which reduces to reversion in algebras $\cl_{p,0}$
and to conjugation in algebras $\cl_{0,q}$. The purpose of this paper is to
bring these concepts together in an attempt to investigate how the algebraic
properties of real Clifford algebras, including their periodicity of eight, are
a direct consequence of the central product structure of Salingaros vee groups
viewed as 2-groups.
