Re: to PTJ

[burroni@math.jussieu.fr]

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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