A SURVEY ON FREE SUBGROUPS IN THE GROUP OF UNITS OF GROUP RINGS-Reference-Cited by-同舟云学术

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

Published:2013-05-09 Issue:06 Volume:12 Page:1350004
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

GONÇALVES JAIRO Z.¹,DEL RÍO ÁNGEL²

Affiliation:

1. Department of Mathematics, University of São Paulo, 05508-090, Brazil

2. Departamento de Matemáticas, Universidad de Murcia, Murcia 30100, Spain

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498813500047

Reference50 articles.

1. Non-Free Points for Groups Generated by a Pair of 2×2 Matrices

2. The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups

3. Commutativity of symmetric elements in group rings

4. On the Group Ring

5. Normal Complements of the Trivial Units in the Unit Group of Some Integral Group Rings

Cited by 10 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Products of unipotent matrices of index 2 over division rings;Acta Mathematica Hungarica;2024-05-06

2. Products of unipotent elements in certain algebras;Forum Mathematicum;2023-05-13

3. Constructing free products of cyclic subgroups inside the group of units of integral group rings;Proceedings of the American Mathematical Society;2023-01-30

4. Abelianization and fixed point properties of units in integral group rings;Mathematische Nachrichten;2022-11-03

5. Units of group rings and a conjecture of H. J. Zassenhaus;São Paulo Journal of Mathematical Sciences;2022-03-04