English

Explicit strong boundedness for higher rank symplectic groups

Group Theory 2023-08-21 v1

Abstract

This paper gives an explicit argument to show strong boundedness for Sp2n(R){\rm Sp}_{2n}(R) for RR 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 SLn{\rm SL}_n to Sp2n{\rm Sp}_{2n}. Further, the presented results solve the question of the asymptotic of strong boundedness for Sp2n(R){\rm Sp}_{2n}(R) for RR semi-local case with an argument that immediately generalizes to all other split Chevalley groups.

Cite

@article{arxiv.2012.12328,
  title  = {Explicit strong boundedness for higher rank symplectic groups},
  author = {Alexander Trost},
  journal= {arXiv preprint arXiv:2012.12328},
  year   = {2023}
}
R2 v1 2026-06-23T21:14:34.187Z