## Structures in Units of Group Rings and Twisted Group Rings Vrije Universiteit Brussel

Denote by Z the integers and let G be a finite multiplicative group. View G as a basis of a "vector space" over Z - this defines the set of elements in the integral group ring ZG, i.e. every element in ZG is a linear combination of elements in G with integral coefficients. As in vector spaces one can define an additive structure on ZG by adding coefficients corresponding to the same basis element. E.g. if g, h are elements in G, then (3g - 2h) + ...