" tommy quaternion "

[tommy1729]

I want to add that in most cases " the candidates " are multiplication tables where the base elements satisfy most of the time the equation :

a*(b*c) = (a*b)*(a*c) up to sign ( +1 or -1 factors )

so we kinda get latin squares with the property of " pseudo self-associative " or " pseudo self-distributive ".

So it is very much connected to virtual knots and latin quandles.

notice how self-associative ( or self-distributive although the other term is more standard ) implies non-associative for a latin square !

The number of latin quandles of size n times n with respect to the factorization of n is therefore very interesting too.
(the factorization of n is like a subgroup/subalgebra thing therefore the research )

Although this clarifies alot , there remain many questions.

iterating self-associative operators also comes to mind, this is also a non common subject just like tetration.

This is post nr 1729 of tommy1729 , hurrah !!!



regards

tommy1729

Tom Marcel Raes

" truth is what does not go away when you stop believing in it. "
tommy1729