Group algebras whose symmetric elements are Lie metabelian

被引：6

作者：

Catino, Francesco ^{[1
]}

Lee, Gregory T. ^{[2
]}

Spinelli, Ernesto ^{[3
]}

机构：

[1] Univ Salento, Dipartimento Matemat Fis & Ennio Giorgi, I-73100 Lecce, Italy

[2] Lakehead Univ, Dept Math Sci, Thunder Bay, ON P7B 5E1, Canada

[3] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, I-00185 Rome, Italy

来源：

FORUM MATHEMATICUM | 2014年 / 26卷 / 05期

关键词：

Group rings; Lie metabelian; involution; symmetric elements; GROUP-RINGS; NILPOTENCY; UNITS;

D O I：

10.1515/forum-2012-0005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F be a field of characteristic p not equal 2 and G a group without 2- elements having an involution *. Write (FG)(+) for the set of elements in the group ring FG that are symmetric with respect to the induced involution. In the present note, we show that if G is finite and (FG)(+) is Lie metabelian, then G is nilpotent. Based on this result, we deduce that if G is torsion, p not equal 3 and (FG)(+) is Lie metabelian, then G must be abelian. This extends a result of Levin and Rosenberger.

引用

页码：1459 / 1471

页数：13

共 15 条

[1]

[Anonymous], 1996, COURSE THEORY GROUPS

[2] Lie derived length and involutions in group algebras [J].