A reduction theorem for the Isomorphism Problem of group algebras over fields

被引：1

作者：

Garcia-Lucas, Diego ^{[1
]}

del Rio, Angel ^{[1
]}

机构：

[1] Univ Murcia, Dept Matemat, Murcia, Spain

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2024年 / 228卷 / 04期

关键词：

Finite groups; Group algebra; Isomorphism problem; MODULAR GROUP-ALGEBRAS; P-GROUPS;

D O I：

10.1016/j.jpaa.2023.107511

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the Isomorphism Problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the Modular Isomorphism Problem reduces to finite modular group algebras.& COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：6

共 43 条

[31] On equivalences between blocks of group algebras: Reduction to the simple components
Marcus, A
JOURNAL OF ALGEBRA, 1996, 184 (02) : 372 - 396
[32] Linear stationary control systems over a Boolean semiring: Geometric properties and the isomorphism problem
O. O. Vasil’ev
N. I. Osetinskii
F. S. Vainshtein
Differential Equations, 2009, 45 : 1783 - 1790
[33] Induced projective modules over group von Neumann algebras
Emmanouil, I
K-THEORY, 2005, 35 (3-4): : 257 - 271
[34] Linear stationary control systems over a Boolean semiring: Geometric properties and the isomorphism problem
Vasil'ev, O. O.
Osetinskii, N. I.
Vainshtein, F. S.
DIFFERENTIAL EQUATIONS, 2009, 45 (12) : 1783 - 1790
[35] Complex group algebras of finite groups:: Brauer's problem 1
Moreto, Alexander
ADVANCES IN MATHEMATICS, 2007, 208 (01) : 236 - 248
[36] Invariant Subsets and Homological Properties of Orlicz Modules over Group Algebras
Uster, Ruya
Oztop, Serap
TAIWANESE JOURNAL OF MATHEMATICS, 2020, 24 (04): : 959 - 973
[37] Units of Group Algebras of Non-Abelian Groups of Order 16 and Exponent 4 over F2k
Gildea, Joe
RESULTS IN MATHEMATICS, 2012, 61 (3-4) : 245 - 254
[38] ON TWISTED GROUP ALGEBRAS OF OTP REPRESENTATION TYPE OVER THE RING OF p-ADIC INTEGERS
Barannyk, Leonid F.
Klein, Dariusz
COLLOQUIUM MATHEMATICUM, 2016, 143 (02) : 209 - 235
[39] Units of some group algebras of groups of order 12 over any finite field of characteristic 3
Gildea, Joe
Monaghan, Faye
ALGEBRA & DISCRETE MATHEMATICS, 2011, 11 (01): : 46 - 58
[40] Zero divisors of support size 3 in group algebras and trinomials divided by irreducible polynomials over GF(2)
Abdollahi, Alireza
Taheri, Zahra
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2021, 145 : 191 - 203

← 1 2 3 4 5 →