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
收藏
页码：166 / 178
页数：12
相关论文
共 50 条
[41]   On Periodic Groups Saturated with Finite Frobenius Groups [J].
Durakov, B. E. ;
Sozutov, A., I .
BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS, 2021, 35 :73-86
[42]   On the central automorphism groups of finite p-groups [J].
Jamali, AR ;
Mousavi, H .
ALGEBRA COLLOQUIUM, 2002, 9 (01) :7-14
[43]   Unit groups of group algebras of groups of order 20 [J].
Ansari, Sheere Farhat ;
Sahai, Meena .
QUAESTIONES MATHEMATICAE, 2021, 44 (04) :503-511
[44]   Metabelian varieties of groups and wreath products of abelian groups [J].
Mikaelian, Vahagn H. .
JOURNAL OF ALGEBRA, 2007, 313 (02) :455-485
[45]   Integral of groups [J].
Filom, Khashayar ;
Miraftab, Babak .
COMMUNICATIONS IN ALGEBRA, 2017, 45 (03) :1105-1113
[46]   Fusions of character tables III: Fusions of cyclic groups and a generalisation of a condition of Camina [J].
Humphries, Stephen P. ;
Kerby, Brent L. ;
Johnson, Kenneth W. .
ISRAEL JOURNAL OF MATHEMATICS, 2010, 178 (01) :325-348
[47]   Wreath products of cyclic p-groups as automorphism groups [J].
Cutolo, G ;
Smith, H ;
Wiegold, J .
JOURNAL OF ALGEBRA, 2004, 282 (02) :610-625
[48]   p-Rank and p-groups in algebraic groups [J].
Deloro, Adrien .
TURKISH JOURNAL OF MATHEMATICS, 2012, 36 (04) :578-582
[49]   Finite Autocapable Groups with the 2-Groups of Maximal Class [J].
Bai, Pengfei ;
Guo, Xiuyun ;
Wang, Jiao .
ALGEBRA COLLOQUIUM, 2024, 31 (04) :651-660
[50]   Extra-special p-groups as groups of automorphisms [J].
De Melo, E. ;
Gomes, M. E. ;
Lima, I .
COMMUNICATIONS IN ALGEBRA, 2023, 51 (02) :475-484
12345