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Let K be a field of characteristic p > 0, K* the multiplicative group of K and $G = G_{p} \times B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $K^{λ} G$ a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable $K^{λ} G$ -module is isomorphic to the outer tensor product V W of an indecomposable $K^{λ} G_{p}$ -module V and a simple...

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

Leonid F. Barannyk, Dariusz Klein (2012)

Colloquium Mathematicae

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 $G = G_{p} \times B$ 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...

Finite groups whose character degree graphs coincide with their prime graphs

Temha Erkoç, Utku Yilmaztürk, İsmail Ş. Güloğlu (2018)

Czechoslovak Mathematical Journal

In the literature, there are several graphs related to a finite group $G$ . Two of them are the character degree graph, denoted by $Δ (G)$ , and the prime graph, $Γ (G)$ . In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs.

Finite groups with a unique nonlinear nonfaithful irreducible character

Ali Iranmanesh, Amin Saeidi (2011)

Archivum Mathematicum

In this paper, we consider finite groups with precisely one nonlinear nonfaithful irreducible character. We show that the groups of order 16 with nilpotency class 3 are the only $p$ -groups with this property. Moreover we completely characterize the nilpotent groups with this property. Also we show that if $G$ is a group with a nontrivial center which possesses precisely one nonlinear nonfaithful irreducible character then $G$ is solvable.

Finite groups with eight non-linear irreducible characters

Yakov Berkovich (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This Note contains the complete list of finite groups, having exactly eight non-linear irreducible characters. In section 4 we consider in full details some typical cases.

Finite Groups with Small Conjugacy Classes.

Carlo Casolo (1994)

Manuscripta mathematica

Finite groups with two rows which differ in only one entry in character tables

Wenyang Wang, Ni Du (2021)

Czechoslovak Mathematical Journal

Let $G$ be a finite group. If $G$ has two rows which differ in only one entry in the character table, we call $G$ an RD1-group. We investigate the character tables of RD1-groups and get some necessary and sufficient conditions about RD1-groups.

Finite $p$ -groups with exactly two nonlinear non-faithful irreducible characters

Yali Li, Xiaoyou Chen, Huimin Li (2019)

Czechoslovak Mathematical Journal

Let $G$ be a finite group with exactly two nonlinear non-faithful irreducible characters. We discuss the properties of $G$ and classify finite $p$ -groups with exactly two nonlinear non-faithful irreducible characters.

Finite subgroups of ${GL}_{24} (ℚ)$ .

Nebe, Gabriele (1996)

Experimental Mathematics

Finite-dimensional twisted group algebras of semi-wild representation type

Leonid F. Barannyk (2010)

Colloquium Mathematicae

Let G be a finite group, K a field of characteristic p > 0, and $K^{λ} G$ the twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for $K^{λ} G$ to be of semi-wild representation type in the sense of Drozd. We also introduce the concept of projective K-representation type for a finite group (tame, semi-wild, purely semi-wild) and we exhibit finite groups of each type.

Five dimensional Bieberbach groups with trivial centre.

Andrzej Szczepanski (1990)

Manuscripta mathematica

Foncteurs de division et structure de $I^{\otimes 2} \otimes Λ^{n}$ dans la catégorie $ℱ$

Aurélien Djament (2007)

Annales de l’institut Fourier

Nous démontrons que dans la catégorie $ℱ$ des foncteurs entre espaces vectoriels sur $𝔽_{2}$ , le produit tensoriel entre le second foncteur injectif standard non constant $V \mapsto 𝔽_{2}^{{(V^{*})}^{\oplus 2}}$ et un foncteur puissance extérieure est artinien. Seul était antérieurement connu le caractère artinien de cet injectif ; notre résultat constitue une étape pour l’étude du troisième foncteur injectif standard non constant de $ℱ$ .Nous utilisons le foncteur de division par le foncteur identité et des considérations issues de la théorie...

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