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On indecomposable projective representations of finite groups over fields of characteristic p > 0

Leonid F. Barannyk, Kamila Sobolewska (2003)

Colloquium Mathematicae

Let G be a finite group, F a field of characteristic p with p||G|, and F λ G the twisted group algebra of the group G and the field F with a 2-cocycle λ ∈ Z²(G,F*). We give necessary and sufficient conditions for F λ G to be of finite representation type. We also introduce the concept of projective F-representation type for the group G (finite, infinite, mixed) and we exhibit finite groups of each type.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

Bartholdi, Laurent, Grigorchuk, Rostislav (2002)

Serdica Mathematical Journal

* The authors thank the “Swiss National Science Foundation” for its support.We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding quasi-regular representations are irreducible. These (infinite-dimensional) representations are approximated by finite-dimensional quasi-regular representations. The Hecke algebras...

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