Wyniki wyszukiwania

1

Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic

100%

Barannyk L., Klein D.

Colloquium Mathematicum

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2012

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tom 129

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nr 2

173-187

EN

Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and $G = G_{p} × B$ 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*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such 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 W.

2

Twisted group rings of strongly unbounded representation type

100%

Barannyk L., Klein D.

Colloquium Mathematicum

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2004

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tom 100

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nr 2

265-287

EN

Let S be a commutative local ring of characteristic p, which is not a~field, S* the multiplicative group of S, W a subgroup of S*, G a finite p-group, and $S^{λ}G$ a twisted group ring of the group G and of the ring S with a~2-cocycle λ ∈ Z²(G,S*). Denote by $Ind_{m}(S^{λ}G)$ the set of isomorphism classes of indecomposable $S^{λ}G$-modules of S-rank m. We exhibit rings $S^{λ}G$ for which there exists a function $f_{λ}: ℕ → ℕ $ such that $f_{λ}(n) ≥ n$ and $Ind_{f_{λ}(n)}(S^{λ}G)$ is an infinite set for every natural n > 1. In special cases $f_{λ}(ℕ)$ contains every natural number m > 1 such that $Ind_{m}(S^{λ}G)$ is an infinite set. We also introduce the concept of projective (S,W)-representation type for the group G and we single out finite groups of every type.

3

On twisted group algebras of OTP representation type over the ring of p-adic integers

100%

Barannyk L., Klein D.

Colloquium Mathematicum

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2016

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tom 143

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nr 2

209-235

EN

Let $ℤ̂_{p}$ be the ring of p-adic integers, $U(ℤ̂_{p})$ the unit group of $ℤ̂_{p}$ and $G = G_{p} × B$ a finite group, where $G_{p}$ is a p-group and B is a p'-group. Denote by $ℤ̂_{p}^{λ}G$ the twisted group algebra of G over $ℤ̂_{p}$ with a 2-cocycle $λ ∈ Z²(G,U(ℤ̂_{p}))$. We give necessary and sufficient conditions for $ℤ̂_{p}^{λ}G$ to be of OTP representation type, in the sense that every indecomposable $ℤ̂_{p}^{λ}G$-module is isomorphic to the outer tensor product V # W of an indecomposable $ℤ̂_{p}^{λ}G_{p}$-module V and an irreducible $ℤ̂_{p}^{λ}B$-module W.

4

On twisted group algebras of OTP representation type

100%

Barannyk L., Klein D.

Colloquium Mathematicum

|

2012

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tom 127

|

nr 2

213-232

EN

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 W.

Ograniczanie wyników

4 Colloquium Mathematicum

4 Barannyk L.

4 Klein D.

1 2016

2 2012

1 2004

Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic

Twisted group rings of strongly unbounded representation type

On twisted group algebras of OTP representation type over the ring of p-adic integers

On twisted group algebras of OTP representation type