This paper investigates the
structure of “generalized Clifford-Littlewood-Eckmann groups”, which arise
in a number of physical applications. They are a direct generalization of
Clifford-Littlewood-Eckmann groups, which have many connections to quadratic
forms and classical Clifford algebras. Here we show that any such group
decomposes into a central product of factor groups of relatively small order,
and that the number of isomorphism types of these factor groups is also
small. The determination of the decomposition of these groups allows an easy
calculation of many of the properties of the groups as well as of their associated
generalized Clifford algebras. These applications will be carried out in subsequent
papers.
