Papers I, II of this projected series lay the algebraic foundations of the theory of the Clifford groups; I deals with the casep> 2, II with the casep= 2. The present introduction refers to both papers. Our theory has applications in group theory, geometry and number theory.

The present paper deals with the Clifford groups in the case p = 2. For the most part, it runs parallel to the previous paper I ([1]) on the case p > 2, and a number of proofs are therefore either given in outline or omitted. A general introduction to both papers is given in I, § 1.

In this paper the Clifford groups PCT(pm), p > 2, PCG(pm) and CS'(pm), and the factor groups ½CS' (pm), which were defined in Paper I of this series (Bolt, Room and Wall [1]), are considered as transformations of projective [pm–1] over the complex field, C. We note that the geometrical results are the same if any of the corresponding groups CT, CG or GG and CS, respectively, are considered instead.

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