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About Units of Group Rings and Codes

Grant number: 12/20138-4
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): February 01, 2013
Effective date (End): January 31, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal researcher:Francisco Cesar Polcino Milies
Grantee:Renata Rodrigues Marcuz Silva
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:09/52665-0 - Groups, rings and algebras: interactions and applications, AP.TEM

Abstract

The study of generating sets for the group of units of group rings is a very active area nowadays. Particularly, in the case of integral group rings, the importance of this research can be compared to Dirichlet's Theorem, for algebraic integers.Unfortunately, there are not general results about generating sets of units for integral group rings. However the researchers have been studying this problem for some types of families of groups. The purpose of this project is to find a set of generators for the group of central units of the following families:1. Z(C2 x ... x C2 x Cp ), where Cm represents the cyclic group of order m;2. Z(Q8 x ... x Q8 x Cp ), with Q8 the quaternion group of order 8;3. Z(D4 x Cp ), with D4 the dihedral group of order 8;4. Z(D4 x ... x D4 x Cp ).