Geodesic
Length of the group algebra of the direct product of a cyclic group and an elementary abelian $p$-group in the modular case
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1132-1144 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, the length of the group algebra of the direct product of a cyclic group and an elementary abelian $p$-group over a field of characteristic $p$ is calculated.
Keywords: finite-dimensional algebras, length of an algebra, abelian groups, $p$-groups.
Mots-clés : group algebras 
@article{SEMR_2024_21_2_a10,
     author = {M. A. Khrystik},
     title = {Length of the group algebra of the direct product of a cyclic group and an elementary abelian $p$-group in the modular case},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1132--1144},
     year = {2024},
     volume = {21},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a10/}
}
TY  - JOUR
AU  - M. A. Khrystik
TI  - Length of the group algebra of the direct product of a cyclic group and an elementary abelian $p$-group in the modular case
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 1132
EP  - 1144
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a10/
LA  - ru
ID  - SEMR_2024_21_2_a10
ER  - 
%0 Journal Article
%A M. A. Khrystik
%T Length of the group algebra of the direct product of a cyclic group and an elementary abelian $p$-group in the modular case
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 1132-1144
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a10/
%G ru
%F SEMR_2024_21_2_a10
M. A. Khrystik. Length of the group algebra of the direct product of a cyclic group and an elementary abelian $p$-group in the modular case. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1132-1144. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a10/

[1] A.E. Guterman, M.A. Khrystik, O.V. Markova, “On the lengths of group algebras of finite abelian groups in the modular case”, J. Algebra Appl., 21:6 (2022), 2250117 | DOI | Zbl

[2] A.E. Guterman, O V. Markova, “The length of group algebras of small-order groups”, J. Math. Sci., New York, 240:6 (2019), 754–761 | DOI | Zbl

[3] A.E. Guterman, O.V. Markova, “The length of the group algebra of the group ${\mathbf Q_8}$”, New trends in algebra and combinatorics, Proceedings of the 3rd International Congress in Algebra and Combinatorics, eds. K.P. Shum, E. Zelmanov, P. Kolesnikov, S.M. Anita Wong, World Sci., Singapore, 2019, 106–134 | DOI

[4] A.E. Guterman, O.V. Markova, M.A. Khrystik, “On the lengths of group algebras of finite abelian groups in the semi-simple case”, J. Algebra Appl., 21:7 (2022), 2250140 | DOI | Zbl

[5] M.A. Khrystik, “Length of the group algebra of the direct product of a cyclic group and a cyclic p-group in the modular case”, J. Math. Sci., New York, 281:2 (2024), 334–341 | DOI | MR

[6] M.A. Khrystik, O.V. Markova, “Length of the group algebra of the dihedral group of order $2^k$”, J. Math. Sci., New York, 255:3 (2021), 324–331 | DOI | Zbl

[7] M.A. Khrystik, O.V. Markova, “On the length of the group algebra of the dihedral group in the semi-simple case”, Commun. Algebra, 50:5 (2022), 2223–2232 | DOI | Zbl

[8] O.V. Markova, “Upper bound for the length of commutative algebras”, Sb. Math., 200:12 (2009), 1767–1787 | DOI | Zbl

[9] O.V. Markova, “An example of length computation for a group algebra of a noncyclic abelian group in the modular case”, J. Math. Sci., New York, 262:5 (2022), 740–748 | DOI | Zbl

[10] O.V. Markova, “The length function and matrix algebras”, J. Math. Sci., New York, 193:5 (2013), 687–768 | DOI | Zbl

[11] C.J. Pappacena, “An upper bound for the length of a finite-dimensional algebra”, J. Algebra, 197:2 (1997), 535–545 | DOI | Zbl

[12] A. Paz, “An application of the Cayley-Hamilton theorem to matrix polynomials in several variables”, Linear Multilinear Algebra, 15 (1984), 161–170 | DOI | Zbl