English

Bounded reduction for Chevalley groups of types $E_6$ and $E_7$

Group Theory 2023-09-26 v2

Abstract

We prove that an element from the Chevalley group of type E6E_6 or E7E_7 over a polynomial ring with coefficients in a small-dimensional ring can be reduced to an element of certain proper subsystem subgroup by a bounded number of elementary root elements. The bound is given explicitly. This result is an effective version of the early stabilisation of the corresponding K1K_1-functor. We also give part of the proof of similar hypothesis for E8E_8.

Keywords

Cite

@article{arxiv.2305.17012,
  title  = {Bounded reduction for Chevalley groups of types $E_6$ and $E_7$},
  author = {Pavel Gvozdevsky},
  journal= {arXiv preprint arXiv:2305.17012},
  year   = {2023}
}

Comments

32 pages, 7 figures, submitted to "European Journal of Mathematics". arXiv admin note: substantial text overlap with arXiv:2106.12697

R2 v1 2026-06-28T10:47:40.233Z