Groups and their integral group rings

Abstract: The integral group ring $\mathbb{Z} G$ of a group $G$ plays an important role in the theory of integral representations. This talk gives a brief introduction to this topic and then shows how such group rings can be investigated using computational tools. In particular, the quotients $I^n(G)/I^{n+1}(G)$, where $I^n(G)$ is the $n$-th power ideal of the augmentation ideal $I(G)$, are an interesting invariant of the group ring $\mathbb{Z} G$ and we show how to determine them for given $n$ and given finitely presented $G$. We then exhibit a variety of example applications for finite and infinite groups $G$.

group theory

Audience: researchers in the topic

GOThIC - Ischia Online Group Theory Conference

Series comments: Please send a message to andrea.caranti@unitn.it to receive a link to the Zoom room where the conference (a series of talks, actually) takes place.