A SURVEY ON FREE SUBGROUPS IN THE GROUP OF UNITS OF GROUP RINGS

被引：12

作者：

Goncalves, Jairo Z. ^{[1
]}

Del Rio, Angel ^{[2
]}

机构：

[1] Univ Sao Paulo, Dept Math, BR-05508090 Sao Paulo, Brazil

[2] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2013年 / 12卷 / 06期

基金：

巴西圣保罗研究基金会;

关键词：

Group rings; free groups; group of units; involutions; free symmetric and unitary units; INTEGRAL GROUP-RINGS; BASS CYCLIC UNITS; BICYCLIC UNITS; FREE-PRODUCTS; SUBNORMAL SUBGROUPS; SYMMETRIC ELEMENTS; NORMAL COMPLEMENTS; LINEAR-GROUPS; FREE PAIRS; CONSTRUCTION;

D O I：

10.1142/S0219498813500047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this survey we revise the methods and results on the existence and construction of free groups of units in group rings, with special emphasis in integral group rings over finite groups and group algebras. We also survey results on constructions of free groups generated by elements which are either symmetric or unitary with respect to some involution and other results on which integral group rings have large subgroups which can be constructed with free subgroups and natural group operations.

引用

页数：28

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