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

2012 ◽  
Vol 129 (2) ◽  
pp. 173-187
Author(s):  
Leonid F. Barannyk ◽  
Dariusz Klein
Keyword(s):  
Finite Groups ◽  
Positive Characteristic ◽  
Projective Representation ◽  
Representation Type ◽  
Valuation Domain ◽  
Discrete Valuation Domain

Godeaux–Serre varieties and the étale index

2013 ◽  
Vol 11 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Benjamin Antieau ◽  
Ben Williams
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Function Fields ◽  
Projective Representation ◽  
High Dimensional ◽  
Index Problem ◽  
Completion Theorem

AbstractWe use Godeaux–Serre varieties of finite groups, projective representation theory, the twisted Atiyah–Segal completion theorem, and our previous work on the topological period-index problem to compute the étale index of Brauer classes α ∈ Brét(X) in some specific examples. In particular, these computations show that the étale index of α differs from the period of α in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Godeaux–Serre varieties in terms of projective representation theory.

scholarly journals Pi-balanced torsion-free modules over a discrete valuation domain

2006 ◽  
Vol 295 (1) ◽  
pp. 269-288 ◽  
Author(s):  
David M. Arnold ◽  
K.M. Rangswamy ◽  
Fred Richman
Keyword(s):  
Valuation Domain ◽  
Discrete Valuation Domain ◽  
Free Modules ◽  
Torsion Free

Degrees of faithful irreducible representations of metabelian groups

2021 ◽  
pp. 2250181
Author(s):  
Rahul Dattatraya Kitture ◽  
Soham Swadhin Pradhan
Keyword(s):  
Normal Subgroup ◽  
Finite Groups ◽  
Positive Characteristic ◽  
Number Fields ◽  
Irreducible Representations ◽  
Modular Representations ◽  
Metacyclic Group ◽  
Metabelian Groups ◽  
Abelian Normal Subgroup ◽  
Field Of Positive Characteristic

In 1993, Sim proved that all the faithful irreducible representations of a finite metacyclic group over any field of positive characteristic have the same degree. In this paper, we restrict our attention to non-modular representations and generalize this result for — (1) finite metabelian groups, over fields of positive characteristic coprime to the order of groups, and (2) finite groups having a cyclic quotient by an abelian normal subgroup, over number fields.

scholarly journals Right weak Engel conditions on linear groups

2019 ◽  
Vol 114 (1) ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Positive Integer ◽  
Linear Group ◽  
Finite Groups ◽  
Characteristic Zero ◽  
Positive Characteristic ◽  
Linear Groups ◽  
Locally Finite ◽  
Class A ◽  
Special Cases ◽  
Prüfer Rank

AbstractIf X is a group-class, a group G is right X-Engel if for all g in G there exists an X-subgroup E of G such that for all x in G there is a positive integer m(x) with [g, nx] ∈ E for all n ≥ m(x). Let G be a linear group. Special cases of our main theorem are the following. If X is the class of all Chernikov groups, or all finite groups, or all locally finite groups, then G is right X-Engel if and only if G has a normal X-subgroup modulo which G is hypercentral. The same conclusion holds if G has positive characteristic and X is one of the following classes; all polycyclic-by-finite groups, all groups of finite Prüfer rank, all minimax groups, all groups with finite Hirsch number, all soluble-by-finite groups with finite abelian total rank. In general the characteristic zero case is more complex.

scholarly journals On the Factorization of Polynomials Over Discrete Valuation Domains

2014 ◽  
Vol 22 (1) ◽  
pp. 273-280
Author(s):  
Doru Ştefănescu
Keyword(s):  
Valuation Domain ◽  
Discrete Valuation Domain ◽  
Valuation Domains ◽  
Univariate Polynomials ◽  
Factorization Of Polynomials

AbstractWe study some factorization properties for univariate polynomials with coefficients in a discrete valuation domain (A,v). We use some properties of the Newton index of a polynomial to deduce conditions on v(ai) that allow us to find some information on the degree of the factors of F.

Representation type of finite groups

1982 ◽  
Vol 20 (6) ◽  
pp. 2515-2528 ◽  
Author(s):  
V. M. Bondarenko ◽  
Yu. A. Drozd
Keyword(s):  
Finite Groups ◽  
Representation Type
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