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 or 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 -functor. We also give part of the proof of similar hypothesis for .
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