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SUMMARY:Bettina Eick (Technical University of Braunschweig)
DTSTART:20201029T160000Z
DTEND:20201029T170000Z
DTSTAMP:20260423T053015Z
UID:GOThIC/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOThIC/4/">G
 roups and their integral group rings</a>\nby Bettina Eick (Technical Unive
 rsity of Braunschweig) as part of GOThIC - Ischia Online Group Theory Conf
 erence\n\n\nAbstract\nThe 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 gro
 up rings can be investigated using computational tools. In particular\, th
 e 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 gr
 oup ring $\\mathbb{Z} G$ and we show how to determine them for given $n$ a
 nd given finitely presented $G$. We then exhibit a variety of example appl
 ications for finite and infinite groups $G$.\n
LOCATION:https://researchseminars.org/talk/GOThIC/4/
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