Generalized Schur Groups

被引：0

作者：

G. K. Ryabov

机构：

[1] Sobolev Institute of Mathematics,

[2] Novosibirsk State Technical University,undefined

来源：

Algebra and Logic | 2023年 / 62卷

关键词：

Schur rings; Schur groups; p-groups; Camina groups; dihedral groups;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

An S-ring (Schur ring) is said to be central if it is contained in the center of a group ring. We introduce the notion of a generalized Schur group, i.e., a finite group such that all central S-rings over this group are Schurian. It generalizes the notion of a Schur group in a natural way, and for Abelian groups, the two notions are equivalent. We prove basic properties and present infinite families of non-Abelian generalized Schur groups.

引用

页码：166 / 178

页数：12

共 50 条

[21] SEPARABILITY OF SCHUR RINGS OVER ABELIAN p-GROUPS
Ryabov, G. K.
ALGEBRA AND LOGIC, 2018, 57 (01) : 49 - 68
[22] CHARACTERIZING FINITE p-GROUPS BY THEIR SCHUR MULTIPLIERS, t(G)=5
Niroomand, Peyman
MATHEMATICAL REPORTS, 2015, 17 (02): : 249 - 254
[23] Generalized Bessel Function Associated with Dihedral Groups
Demni, Nizar
JOURNAL OF LIE THEORY, 2012, 22 (01) : 81 - 91
[24] On the number of solutions of a generalized commutator equation in finite groups
Nath, R. K.
Prajapati, S. K.
ACTA MATHEMATICA HUNGARICA, 2018, 156 (01) : 18 - 37
[25] Weak Cayley tables and generalized centralizer rings of finite groups
Humphries, Stephen P.
Rode, Emma L.
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2012, 153 : 281 - 318
[26] Schur multipliers and the Lazard correspondence
Eick, Bettina
Horn, Max
Zandi, Seiran
ARCHIV DER MATHEMATIK, 2012, 99 (03) : 217 - 226
[27] On dimension of the Schur multiplier of nilpotent Lie algebras
Niroomand, Peyman
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2011, 9 (01): : 57 - 64
[28] Schur rings over infinite dihedral group
Chen, Gang
He, Jiawei
Wu, Zhiman
COMMUNICATIONS IN ALGEBRA, 2024, 52 (06) : 2534 - 2542
[29] The unitary cover of a finite group and the exponent of the Schur multiplier
Sambonet, Nicola
JOURNAL OF ALGEBRA, 2015, 426 : 344 - 364
[30] ON INFINITE CAMINA GROUPS
Herzog, Marcel
Longobardi, Patrizia
Maj, Mercede
COMMUNICATIONS IN ALGEBRA, 2011, 39 (11) : 4403 - 4419

← 1 2 3 4 5 →