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}
}
  • Pavel Gvozdevsky
  • Published 26 August 2020
  • Mathematics
  • Journal of Mathematical Sciences
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

The word maps w˜:GLmD2k→GLnD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}

Список литературы

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

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

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

Sums of orbits of algebraic groups I

On the conjectures of J. Thompson and O. Ore

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

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

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

Estimates of extended covering numbers are obtained for Chevalley groups over local rings. §