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Bounded generation by root elements is a property which has been widelystudied for various types of linear algebraic groups defined over rings ofintegers in algebraic number fields. However, when considering global functionfields, there are not many results beyond the treatment of special cases due toNica and Queen. In this paper, we use model theoretic methods due to Carter,Keller and Paige written up by Morris to prove bounded generation by rootelements for simply connected, split Chevalley groups defined over the ring ofall integers in a global function field. We further apply this boundedgeneration result together with results from a previous paper by the author toderive that the aforementioned Chevalley groups satisfy the strong boundednessproperty introduced by Kedra, Libman and Martin.

Bounded generation by root elements for Chevalley groups defined over rings of integers of function fields with an application in strong boundedness