Group rings with metabelian unit groups

被引：1

作者：

Juhasz, Tibor ^{[1
]}

Spinelli, Ernesto ^{[2
]}

机构：

[1] Eszterhazy Karoly Catholic Univ, Inst Math & Informat, Lednyka U 4, H-3300 Eger, Hungary

[2] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2022年 / 226卷 / 06期

关键词：

Group rings; Unit group; Derived length; GROUP-ALGEBRAS;

D O I：

10.1016/j.jpaa.2021.106946

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F be a field of odd characteristic and G a group. In 1991 Shalev established necessary and sufficient conditions so that the unit group of the group ring FG is metabelian when G is finite. Here, in the modular case, we do the same without restrictions on G. In particular, new cases emerge when G contains elements of infinite order. (c) 2021 Elsevier B.V. All rights reserved.

引用

页数：11

共 50 条

[31] Unit Groups of Integral Group Rings: Old and New
Kimmerle W.
Jahresbericht der Deutschen Mathematiker-Vereinigung, 2013, 115 (2) : 101 - 112
[32] The ranks of central unit groups of integral group rings of alternating groups
Aleev R.Z.
Kargapolov A.V.
Sokolov V.V.
Journal of Mathematical Sciences, 2010, 164 (2) : 163 - 167
[33] ON UNIT GROUP OF FINITE SEMISIMPLE GROUP ALGEBRAS OF NON-METABELIAN GROUPS UP TO ORDER 72
Mittal, Gaurav
Sharma, Rajendra Kumar
MATHEMATICA BOHEMICA, 2021, 146 (04): : 429 - 455
[34] TORSION UNITS IN INTEGRAL GROUP-RINGS OF SOME METABELIAN-GROUPS .2.
MARCINIAK, Z
RITTER, J
SEHGAL, SK
WEISS, A
JOURNAL OF NUMBER THEORY, 1987, 25 (03) : 340 - 352
[35] On the prime graph of the unit group of integral group rings of finite groups
Kimmerle, W.
Groups, Rings and Algebras, 2006, 420 : 215 - 228
[36] Free products of abelian groups in the unit group of integral group rings
Jespers, E
Leal, G
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (05) : 1257 - 1265
[37] UNIT GROUP OF INTEGRAL GROUP-RINGS OF METACYCLIC FROBENIUS GROUPS
ROGGENKAMP, KW
ARCHIV DER MATHEMATIK, 1980, 35 (03) : 263 - 266
[38] Lie centrally metabelian group rings in characteristic 3
Kulshammer, B
Sharma, RK
JOURNAL OF ALGEBRA, 1996, 180 (01) : 111 - 120
[39] Zassenhaus Conjecture (ZC1) on torsion units of integral group rings for some metabelian groups
Ángel del Río
Sudarshan K. Sehgal
Archiv der Mathematik, 2006, 86 : 392 - 397
[40] Small ranks of central unit groups of integral group rings of alternating groups
Aleev, R. Zh.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2014, 285 : S12 - S18

← 1 2 3 4 5 →