Abstract
Publisher Summary This chapter discusses the general construction method of kinematic structures by means of a commutative kinematic space A and a suitable monomorphism semigroup M of A. A kinematic space is a group (G,•) with a suitable incidence structure (G,L) where every left and right translation: a l : G→G, x → ax and a r : G→G, x→xa; with a e G, is an automorphism of (G,L) and where every line through 1 is a subgroup. If the group (G,•) is commutative, the kinematic space is just a translation structure. In a more general sense, kinematic spaces are obtained from a suitable class of translation structures. A further equivalence relation in the line-set can be derived such that Euclid's axiom is fulfilled. This second parallelism makes then the translation structure to a double parallelism space such that the additional conditions for kinematic spaces are fulfilled.
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