let S be a set of s elements. Let F be a 3-placed operator...

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Question by redwasp
Submitted on 8/26/2003
Related FAQ: sci.math FAQ: Who is Bourbaki?
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let S be a set of s elements. Let F be a 3-placed operator that works on these elements. It may be observed that all elements of S have a threefold result for that operator, each of the results being a sXs matrix. Suppose the operator F(p,q,r) creates a groups-structure in S for every fixed p, q and r belonging to S. Has someone until now studied this structure (a groups of 3 dimensions)? and where can i find publications on the subject? Is there something as a multi-dimensional group theory? I think that every m dimensional group can be represented by an n dimensional group (with m>n) of objects of m-n dimensions in exactly m-n different ways. is this correct? is it proovable?

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