About Units of Group Rings and Codes

• Grant number: 12/20138-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2013
• End date: January 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Francisco Cesar Polcino Milies
• Grantee: Renata Rodrigues Marcuz Silva
• Host 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 ).