Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 1, pp. 2546 (2009) 

On groups with root system of type $^{2}F_{4}$H. OueslatiMathematisches Institut, JustusLiebigUniversität Gießen, Arndtstra\"ss e 2, D35392 Gie\"ss en, GermanyAbstract: Let $\tilde{\Phi}$ be a root system of type $^{2}F_{4}$, and let $G$ be a group generated by nontrivial subgroups $A_{r}$, $r\in\tilde{\Phi}$, satisfying some generalized Steinberg relations, which are also satisfied by root subgroups corresponding to a Moufang octagon. These relations can be considered as a generalization of the elementwise commutator relations in Chevalley groups. The Steinberg presentation specifies the groups satisfying the Chevalley commutator relations. In the present paper some sort of generalized Steinberg presentation for groups with root system of type $^{2}F_{4}$ is provided. As a main result we classify the possible structures of $G$. Full text of the article:
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