Results 181 to 190 of about 2,589 (216)

On integral representations of finite groups and rings generated by character values

Journal of Algebra and Its Applications, 2022
We study realization fields and integrality of characters of finite subgroups of [Formula: see text] and related lattices with a focus on the integrality of characters of finite groups [Formula: see text]. We are interested in the arithmetic aspects of the integral realizability of representations of finite groups, order generated by the character ...
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CROSSED GROUP RINGS OF FINITE GROUPS AND RINGS OF $ p$-ADIC INTEGERS WITH FINITELY MANY INDECOMPOSABLE INTEGRAL REPRESENTATIONS

Mathematics of the USSR-Sbornik, 1980
Let be a finite extension of the field of rational -adic numbers, the ring of all integral elements of , the multiplicative group of , a finite group, and the crossed group ring of and with the factor system (; ). A classification is given of the rings for which the number of indecomposable -representations is finite. When is a group ring, this problem
Barannik, L. F., Gudivok, P. M.
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On the Classification of Local Integral Representations of Finite Abelian p-Groups

Lecture Notes in Mathematics, 1975
exaly   +2 more sources

On the integral and globally irreducible representations of finite groups

Journal of Algebra and Its Applications, 2018
We consider the arithmetic of integral representations of finite groups over algebraic integers and the generalization of globally irreducible representations introduced by Van Oystaeyen and Zalesskii. For the ring of integers [Formula: see text] of an algebraic number field [Formula: see text] we are interested in the question: what are the conditions
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Galois Stability, Integrality and Realization Fields for Representations of Finite Abelian Groups

Algebras and Representation Theory, 2003
Let \(E/F\) be a finite Galois extension of fields and \(G\) a finite Abelian subgroup of \(\text{GL}_n(E)\), which is \(G_{E/F}\)-stable. The paper resumes earlier work of the author and proves the existence of such \(G\) so that \(E\) is the field \(F(G)\) generated by the matrix entries of \(G\) over \(F\), provided that some natural conditions on \(
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On P-adic integral representations of a finite group.

1952
It has been shown by F.E. Diederichsen that for integral representations of a finite group, the irreducible constituents in any complete reduction are note necessarily unique up to order and unimodular equivalence. In this same article, it is shown that for certain finite groups, such as the cyclic group of order 4, there are infinitely many classes of
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Representations of finite p-groups over the ring of formal power series with integral p-adic coefficients

Ukrainian Mathematical Journal, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gudivok, P. M., Oros, V. M., Rojter, A. V.   +2 more
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Galois stability for integral representations of finite groups

2001
Let \(E/F\) be a Galois extension of number fields with Galois group \(\Gamma\), \(R\subset E\) a Dedekind ring (or \(E\) itself), and \(G\subset\text{GL}_n(R)\) a finite \(\Gamma\)-stable subgroup. In the paper the following question is considered: what kind of restrictions on the field \(E\) are implied by the \(\Gamma\)-stability of \(G\), and for ...
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The relationship between arithmetics and infinite series of indecomposable integral representations of finite groups

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1984
Assuming Artin's conjecture on primitive roots, the author constructs some infinite sets of integral representations of certain finite p- groups. The methods are extended from those of \textit{S. D. Berman} and \textit{P. M. Gudivok} [Izv. Akad. Nauk SSSR, Ser. Mat. 28, 875-910 (1964; Zbl 0207.335)].
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Finite Range Integral Representation of Sommerfeld Integral for Homogeneous Dielectric Half-Space and Complete Uniform Asymptotic Expansion

IEEE Transactions on Antennas and Propagation, 2021
Il-Suek Koh
exaly