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CONSTRUCTION OF COMMUTATOR BLUEPRINTS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 03 November 2025, pp. 1-33
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- Article
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Commutator blueprints can be seen as blueprints for constructing RGD systems over
$\mathbb {F}_2$ with prescribed commutation relations. In this paper, we construct several families of Weyl-invariant commutator blueprints, mostly of universal type. Also applying another result of the author, we obtain new examples of exotic RGD systems of universal type over 
$\mathbb {F}_2$. In particular, we generalize Tits’ construction of uncountably many trivalent Moufang twin trees to higher rank, we obtain an example of an RGD system of rank 
$3$ such that the nilpotency degree of the groups 
$U_w$ is unbounded, and we construct a commutator blueprint of type 
$(4, 4, 4)$ that is used to answer a question of Tits from the late 
$1980$s about twin buildings.
