Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 1, pp. 25-46 (2009)

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On groups with root system of type $^{2}F_{4}$

H. Oueslati

Mathematisches Institut, Justus-Liebig-Universität Gießen, Arndtstra\"ss e 2, D-35392 Gie\"ss en, Germany

Abstract: Let $\tilde{\Phi}$ be a root system of type $^{2}F_{4}$, and let $G$ be a group generated by non-trivial 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 element-wise 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 $G$.

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Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.

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