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On commutative twisted group rings

Todor Zh. Mollov, Nako A. Nachev (2005)

Czechoslovak Mathematical Journal

Let G be an abelian group, R a commutative ring of prime characteristic p with identity and R t G a commutative twisted group ring of G over R . Suppose p is a fixed prime, G p and S ( R t G ) are the p -components of G and of the unit group U ( R t G ) of R t G , respectively. Let R * be the multiplicative group of R and let f α ( S ) be the α -th Ulm-Kaplansky invariant of S ( R t G ) where α is any ordinal. In the paper the invariants f n ( S ) , n { 0 } , are calculated, provided G p = 1 . Further, a commutative ring R with identity of prime characteristic p is said...

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 local weak crossed product orders

Th. Theohari-Apostolidi, A. Tompoulidou (2014)

Colloquium Mathematicae

Let Λ = (S/R,α) be a local weak crossed product order in the crossed product algebra A = (L/K,α) with integral cocycle, and H = σ G a l ( L / K ) | α ( σ , σ - 1 ) S * the inertial group of α, for S* the group of units of S. We give a condition for the first ramification group of L/K to be a subgroup of H. Moreover we describe the Jacobson radical of Λ without restriction on the ramification of L/K.

On twisted group algebras of OTP representation type

Leonid F. Barannyk, Dariusz Klein (2012)

Colloquium Mathematicae

Assume that S is a commutative complete discrete valuation domain of characteristic p, S* is the unit group of S and G = G p × B is a finite group, where G p is a p-group and B is a p’-group. Denote by S λ G the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). We give necessary and sufficient conditions for S λ G to be of OTP representation type, in the sense that every indecomposable S λ G -module is isomorphic to the outer tensor product V W of an indecomposable S λ G p -module V and an irreducible S λ B -module...

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