Some characterizations of Moufang generalized quadrangles

We prove the longstanding conjecture that the 3-Moufang condition for generalized quadrangles is equivalent to the Moufang condition. We mention some other characterizations of Moufang quadrangles that follow from this result. We also provide a short proof of Tent's recent result that every half Moufang quadrangle is necessarily a Moufang quadrangle.

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