Commutator Lengths in General Linear Group Over a Skew-Field
@article{Gvozdevsky2020CommutatorLI,
title={Commutator Lengths in General Linear Group Over a Skew-Field},
author={Pavel Gvozdevsky},
journal={Journal of Mathematical Sciences},
year={2020},
volume={264},
pages={29 - 38}
}Upper and lower estimates for the maximal commutator length of a noncentral element of the elementary subgroup of the general linear group over a skew-field are proved on the basis the maximal commutator length of an element of the multiplicative group of this skew-field.
References
SHOWING 1-10 OF 17 REFERENCES
Products of Commutators on a General Linear Group Over a Division Algebra
- Materials ScienceJournal of Mathematical Sciences
- 2019
The word maps w˜:GLmD2k→GLnD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…
Список литературы
- Physics
- 1601
into planar Created and studied selective photosensitive structures based on Au-AlGaN Schottky barrier fo r the ultraviolet range of the spectrum. The methods of spectrum management photosensitivity…
Gauss decomposition with prescribed semisimple part in chevalley groups iii: Finite twisted groups
- Mathematics
- 1996
Continuing the investigations of [EG] and [EGII], we shall show that Theorem 1 below is also valid for twisted CheMLley groups over finite fields. Let G be such a group. Here we consider only groups…
Gauss Decomposition with Prescribed Semisimple Part in Quadratic Groups
- Mathematics
- 2009
Quadratic groups, whose definitions depend on form parameters, contain the orthogonal groups, symplectic groups, classical unitary groups and all the classical groups of Dieudonné [4] as well as…
On the conjectures of J. Thompson and O. Ore
- Mathematics
- 1998
If G is a finite simple group of Lie type over a field containing more than 8 elements (for twisted groups 'Xn (ql) we require q > 8, except for 2B2(q2), 2G2(q2), and 2 F4 (q2), where we assume q2 >…
Word maps on perfect algebraic groups
- MathematicsInt. J. Algebra Comput.
- 2018
Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups is extended and Borel’s theorem to some words with constants is generalized.
Gauss decomposition for Chevalley groups, revisited
- Mathematics
- 2011
In the 1960's Noboru Iwahori and Hideya Matsumoto, Eiichi Abe and Kazuo Suzuki, and Michael Stein discovered that Chevalley groups $G=G(Phi,R)$ over a semilocal ring admit remarkable Gauss…
Products of conjugacy classes in Chevalley groups over local rings
- Mathematics
- 2006
Estimates of extended covering numbers are obtained for Chevalley groups over local rings. §