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arXiv · 2012.12328

Explicit strong boundedness for higher rank symplectic groups

Alexander Trost
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Abstract

This paper gives an explicit argument to show strong boundedness for ${\rm Sp}_{2n}(R)$ for $R$ a ring of S-algebraic integers or a semi-local ring. This gives a quantitative version of a related abstract result in a previous paper of the author. The results presented further generalize older results regarding strong boundedness by Kedra, Libman and Martin and Morris from ${\rm SL}_n$ to ${\rm Sp}_{2n}$. Further, the presented results solve the question of the asymptotic of strong boundedness for ${\rm Sp}_{2n}(R)$ for $R$ semi-local case with an argument that immediately generalizes to all other split Chevalley groups.

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BibTeXRIS

Alexander Trost. 2020-12-22. Explicit strong boundedness for higher rank symplectic groups. https://doi.org/10.1016/j.jalgebra.2022.03.041

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