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In this paper we prove that an RGD-system over F_2 with prescribed commutation relations exists if and only if the commutation relations are Weyl-invariant and can be realized in the group U_+ . This result gives us a machinery to produce new examples of RGD-systems with complicated commutation relations. We also discuss some applications of this result.

An RGD system \\(D\\) is called linear w.r.t. a root basis \\(B\\) if the commutation relations between the root groups of \\(D\\) are `linear' in a certain sense. Moreover, \\(D\\) is called linearizable, if there exists a root basis \\(B\\) such that \\(D\\) is linear w.r.t. \\(B\\). For many examples of RGD systems it is easy to see that they are linear w.r.t. a concrete root basis. To the best of our knowledge, it was unclear whether RGD systems exist which are not linearizable. In this article we show that there exist uncountably many RGD systems which are not linearizable. In particular, we provide the first explicit example of such an RGD system. This expands the quote from Rémy that axiom (RGD\\(1\\))\\(_lin\\) is not only a strengthening of axiom (RGD\\(1\\)), but is in fact stronger than it. We show that non-linearizability appears in examples of universal type, and also in examples of \\(2\\)-spherical type. For the examples of universal type we construct an uncountable family of non-linearizable RGD systems, and for the examples of \\(2\\)-spherical type we show that the RGD systems of type \\((4, 4, 4)\\) recently constructed by the author provide uncountably many non-linearizable RGD systems.

In this article we work out the details of flat groups of the automorphism group of locally finite Bruhat-Tits buildings.

In this paper we show that Weyl-invariant commutator blueprints of type \\((4, 4, 4)\\) are faithful. As a consequence we answer a question of Tits from the late \\(1980\\)s about twin buildings. Moreover, we obtain the first example of a \\(2\\)-spherical Kac-Moody group over a finite field which is not finitely presented.

In this paper we prove that the group \\(U_+\\) of an RGD-system of type \\((4, 4, 4)\\) over \\(F_2\\) contains a certain tree product as a subgroup. The proof relies on a careful analysis of the action on the associated twin building. This result is part of a larger project and we will use it as an induction start to construct uncountably many RGD-systems of type \\((4, 4, 4)\\) over \\(F_2\\).

In CM06 Caprace and Mühlherr solved the isomorphism problem for Kac-Moody groups of non-spherical type over finite fields of cardinality at least \\(4\\). In this paper we solve the isomorphism problem for RGD-systems (e.g.\\ Kac-Moody groups) over \\(F_2\\) whose type is \\(2\\)-complete and \\(A_2\\)-free.

• Surface properties of aerial plant organs have been shown to affect the interaction of fungal plant pathogens and their hosts. Conidial germination and differentiation - the so‐called prepenetration processes - of the barley powdery mildew fungus (Blumeria graminis f. sp. hordei) are known to be triggered by n‐hexacosanal (C₂₆‐aldehyde), a minor constituent of barley leaf wax. • In order to analyze the differentiation‐inducing capabilities of typical aldehyde wax constituents on conidia of wheat and barley powdery mildew, synthetic even‐numbered very‐long‐chain aldehydes (C₂₂-C₃₀) were assayed, applying an in vitro system based on Formvar®/n‐hexacosane‐coated glass slides. • n‐Hexacosanal was the most effective aldehyde tested. Germination and differentiation rates of powdery mildew conidia increased with increasing concentrations of very‐long‐chain aldehydes. Relative to n‐hexacosanal, the other aldehyde compounds showed a gradual decrease in germination‐ and differentiation‐inducing capabilities with both decreasing and increasing chain length. • In addition to n‐hexacosanal, several other ubiquitous very‐long‐chain aldehyde wax constituents were capable of effectively stimulating B. graminis prepenetration processes in a dose‐ and chain length‐dependent manner. Other wax constituents, such as n‐alkanes, primary alcohols (with the exception of n‐hexacosanol), fatty acids and alkyl esters, did not affect fungal prepenetration.

Commutator blueprints can be seen as blueprints for constructing RGD-systems over \\(F_2\\) with prescribed commutation relations. In this paper we construct several families of Weyl-invariant commutator blueprints, mostly of universal type. Together with the main result of BiRGD we obtain new examples of exotic RGD-systems of universal type over \\(F_2\\).

In this paper we prove that an RGD-system over \\(F_2\\) with prescribed commutation relations exists if and only if the commutation relations are Weyl-invariant and can be realized in the group \\(U_+\\). This result gives us a machinery to produce new examples of RGD-systems with complicated commutation relations. We also discuss some applications of this result.

Commutator blueprints can be seen as blueprints for constructing RGD-systems over \\(F_2\\) with prescribed commutation relations. In this paper we construct several families of Weyl-invariant commutator blueprints, mostly of universal type. Together with the main result of BiRGD we obtain new examples of exotic RGD-systems of universal type over \\(F_2\\).