Hi, You can find this equation (and ref to Higman and Neumann) in the GTM springer no 26 page 7 : E.G. manes "Algebraic Theory. xxxdydzdxxdxdzddd=y (polish notations and d is the binary operation.) Best, Albert "Joyal, André" <joyal.andre@uqam.ca> a écrit :
Hi Peter,
And, as someone (I forget who, but it may have been Mike Barr) pointed out long ago, one can (well, almost) define the variety of groups as the variety defined by a single binary operation satisfying a single equation; 1 < 3, but no sane group-theorist would do it that way.
I recall that Tarski is responsible for describing the theory of groups with a single binary operation satisfying a single equation. But dont have a reference with me.
A small point: the algebraic theory described by Tarski admits the empty set as a model. Strictly speaking, it is not equivalent to the theory of group.
Best, André
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