Geodesic
Length of the group algebra of the direct product of a cyclic group and a cyclic $p$-group in the modular case
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 166-176 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper, the length of the group algebra of the direct product of a cyclic group and a cyclic $p$-group over a field of characteristic $p$ is calculated. A general lower bound for the length of a commutative group algebra is proved, and in the case of the direct product of a cyclic group and a cyclic $p$-group this bound is sharp. 
@article{ZNSL_2023_524_a11,
     author = {M. A. Khrystik},
     title = {Length of the group algebra of the direct product of a cyclic group and a cyclic $p$-group in the modular case},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {166--176},
     year = {2023},
     volume = {524},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a11/}
}
TY  - JOUR
AU  - M. A. Khrystik
TI  - Length of the group algebra of the direct product of a cyclic group and a cyclic $p$-group in the modular case
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 166
EP  - 176
VL  - 524
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a11/
LA  - ru
ID  - ZNSL_2023_524_a11
ER  - 
%0 Journal Article
%A M. A. Khrystik
%T Length of the group algebra of the direct product of a cyclic group and a cyclic $p$-group in the modular case
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 166-176
%V 524
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a11/
%G ru
%F ZNSL_2023_524_a11
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. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 166-176. http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a11/

[1] A. E. Guterman, O. V. Markova, “Dlina gruppovykh algebr grupp nebolshogo razmera”, Zap. nauchn. semin. POMI, 472, 2018, 76–87

[2] O. V. Markova, “Verkhnyaya otsenka dliny kommutativnykh algebr”, Matem. sb., 200:12 (2009), 41–62 | DOI | Zbl

[3] O. V. Markova, “Primer vychisleniya dliny gruppovoi algebry netsiklicheskoi abelevoi gruppy v modulyarnom sluchae”, Fund. prikl. matem., 23:2 (2020), 217–229

[4] O. V. Markova, “Funktsiya dliny i matrichnye algebry”, Fund. prikl. matem., 17:6 (2012), 65–173

[5] O. V. Markova, M. A. Khrystik, “Dlina gruppovoi algebry gruppy diedra poryadka $2^k$”, Zap. nauchn. semin. POMI, 496, 2020, 169–181

[6] 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), 2250117–2250130 | DOI | MR

[7] 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, A. Wong, World Sci., Singapore, 2019, 106–134 | MR

[8] 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), 2250140–2250153 | DOI | MR

[9] 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 | MR | Zbl

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

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