Vertices of indecomposable modules, as defined by J. A. Green, play a major role in the representation theory of finite groups. Vertices of irreducible
characters for \(p\)-solvable finite groups were defined by G. Navarro and,
in somewhat greater generality, by C. Eaton. In my talk, I will report on recent joint work with R. Kessar and M. Linckelmann on \(p\)-subgroups of a
finite group \(G\) which can be attached to irreducible characters of \(G\) and
which are related to Green's and Navarro's vertices. The investigation of these \(p\)-subgroups leads to questions concerning the group ring \(RG\) (where
\(R\) is a suitable complete discrete valuation ring) and related \(R\)-orders.
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