This analysis demonstrates subgroup structures in RGD-systems of type (4, 4, 4), indicating broader implications for infinite constructions.
In this paper we prove that the group U₊ of an RGD-system of type $(4, 4, 4)$ over F₂ 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 F₂.
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Sebastian Bischof (2025) studied this question.
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