Geodesic
A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 165-174.

Voir la notice de l'article provenant de la source Math-Net.Ru

We find necessary and sufficient universality conditions of a matrix from the unitriangular matrix group of arbitrary finite dimension over a commutative associative ring with unity. An algorithm is used to determine the universality of the element of the unitriangular matrix group over the ring of polynomials with a finite number of variables with integer coefficients.
Mots-clés : unitriangular matrix group
Keywords: derived subgroup, universal element, ring, Euclidean ring. 
@article{SEMR_2019_16_a1,
     author = {N. G. Khisamiev and S. D. Tynybekova and A. A. Konyrkhanova},
     title = {A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {165--174},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a1/}
}
TY  - JOUR
AU  - N. G. Khisamiev
AU  - S. D. Tynybekova
AU  - A. A. Konyrkhanova
TI  - A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 165
EP  - 174
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a1/
LA  - ru
ID  - SEMR_2019_16_a1
ER  - 
%0 Journal Article
%A N. G. Khisamiev
%A S. D. Tynybekova
%A A. A. Konyrkhanova
%T A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 165-174
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a1/
%G ru
%F SEMR_2019_16_a1
N. G. Khisamiev; S. D. Tynybekova; A. A. Konyrkhanova. A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 165-174. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a1/

[1] M.I. Kargapolov, Yu.I. Merzlyakov, Foundations of groups theory, M., “Nauka” | MR

[2] A. Bier, “The width of verbal subgroups in the group of unitriangular matrices over a field”, Int. J. Alg. Comput., 22:3 (2012), 21–41 | DOI | MR

[3] N.S. Bahta, “On the representability of the commutator of group $UT(n,K)$ by the set of values of one variable”, Herald of Omsk University, 2 (2012), 44–46

[4] N.S. Bahta, “On representability of members of the low central series of the group $UT(n,K)$ by values of one-variable function”, Herald of Omsk University, 4 (2013), 13–15

[5] A.V. Men’shov, V.A. Roman’kov, “On p-solvability of some regular equations over a Heisenberg p-group”, Herald of Omsk University, 3 (2014), 11–14 | Zbl

[6] V.A. Roman’kov, “Equations over groups”, Groups Complexity Cryptology, 2:4 (2012), 191–240 | MR

[7] L.L. Konyrkhanova, “Universal elements of the groups of unitriangular matrices over a field”, Herald of Omsk University, 4 (2015), 18–20

[8] L.L. Konyrkhanova, “Universal elements of unitriangular matrices groups over ring of integers”, Herald of Omsk University, 2 (2016), 11–13

[9] L.L. Konyrkhanova, V.A. Roman'kov, “On solvability of commutator equations in Lie algebras”, Bulletin of the Karaganda University. Mathematics series, 1 (2017), 57–64

[10] L.L. Konyrkhanova, N.G. Khisamiev, “Universal elements of unitriangular matrices groups”, Bulletin of the Karaganda University. Mathematics series, 2 (2017), 79–85