Geodesic
Commutator lengths in general linear group over a skew-field
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 45-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We give an upper and lower estimate for the maximal commutator length of a noncentral element of the elementary subgroup of the general linear group over a skew-field based on the maximal commutator length of an element of the multiplicative group of that skew-field. 
@article{ZNSL_2020_492_a3,
     author = {P. B. Gvozdevsky},
     title = {Commutator lengths in general linear group over a skew-field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {45--60},
     year = {2020},
     volume = {492},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a3/}
}
TY  - JOUR
AU  - P. B. Gvozdevsky
TI  - Commutator lengths in general linear group over a skew-field
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 45
EP  - 60
VL  - 492
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a3/
LA  - ru
ID  - ZNSL_2020_492_a3
ER  - 
%0 Journal Article
%A P. B. Gvozdevsky
%T Commutator lengths in general linear group over a skew-field
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 45-60
%V 492
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a3/
%G ru
%F ZNSL_2020_492_a3
P. B. Gvozdevsky. Commutator lengths in general linear group over a skew-field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 45-60. http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a3/

[1] E. Artin, Geometricheskaya algebra, Nauka, M., 1969

[2] N. L. Gordeev, B. E. Kunyavskii, E. B. Plotkin, “Verbalnye otobrazheniya i verbalnye otobrazheniya s konstantami prostykh algebraicheskikh grupp”, Doklady RAN, 471:2 (2016), 136–138 | Zbl

[3] E. A. Egorchenkova, Verbalnye otobrazheniya prostykh algebraicheskikh grupp nad beskonechnymi polyami, Kandidatskaya dissertatsiya, Sankt-Peterburg, 2019

[4] E. A. Egorchenkova, N. L. Gordeev, “Proizvedeniya kommutatorov polnoi lineinoi gruppy nad telom”, Zap. nauchn. semin. POMI, 470, 2018, 88–104

[5] V. V. Kursov, “O kommutante polnoi lineinoi gruppy nad telom”, Dokl. AN BSSR, 1979, 869–871 | MR | Zbl

[6] V. V. Kursov, Kommutatornye svoistva lineinykh grupp, Kandidatskaya dissertatsiya, Minsk, 1984 | Zbl

[7] Z. I. Borevich, “Parabolic subgroups in linear groups over a semilocal ring”, Vestnik Leningrad. Univ., 1976, no. 13, 16–24 | MR | Zbl

[8] V. Chernousov, E. W. Ellers, N. Gordeev, “Gauss decomposition with prescribed semisimple part: short proof”, J. Algebra, 229:1 (2000), 314–332 | DOI | MR | Zbl

[9] Ellers E. W., Gordeev N., “Gauss decomposition with prescribed semisimple part in Chevalley groups. III. Finite twisted groups”, Comm. Algebra, 24:14 (1996), 4447–4475 | DOI | MR | Zbl

[10] E. W. Ellers, N. Gordeev, “On the conjectures of J. Thompson and O. Ore”, Trans. Amer. Math. Soc., 350 (1998), 3657–3671 | DOI | MR | Zbl

[11] N. Gordeev, “Sums of orbits of algebraic groups. I”, J. Algebra, 295:1 (2006), 62–80 | DOI | MR | Zbl

[12] N. L. Gordeev, J. Saxl, “Products of conjugacy classes in Chevalley groups over local rings”, Algebra i analiz, 17:2 (2005), 96–107 | MR

[13] C. Y. Hui, M. Larsen, A. Shalev, “The Waring problem for Lie groups and Chevalley groups”, Israel J. Math., 210 (2015), 81–100 | DOI | MR | Zbl

[14] J. Morita, E. Plotkin, “Prescribed Gauss decompositions for Kac–Moody groups over fields”, Rend. Semin. Mat. Univ. Padova, 106 (2001), 153–163 | MR | Zbl

[15] N. Gordeev, B. Kunyavskii, E. Plotkin, “Word maps on perfect algebraic groups”, International Journal of Algebra and Computation, 28 (2018), 1487–1515 | DOI | MR | Zbl

[16] N. Gordeev, B. Kunyavskii, E. Plotkin, “Word maps, word maps with constants and representation varieties of one-relator groups”, J. Algebra, 500 (2018), 390–424 | DOI | MR | Zbl

[17] A. Smolensky, B. Sury, N. Vavilov, “Gauss decomposition for Chevalley groups, revisited”, International J. Group Theory, 1:1 (2012), 3–16 | MR | Zbl

[18] S.-K. Ye, S. Chen, C.-S. Wang, “Gauss decomposition with prescribed semisimple part in quadratic groups”, Comm. Algebra, 37 (2009), 3054–3063 | DOI | MR | Zbl