On the integral and globally irreducible representations of finite groups

Dmitry Malinin

doi:10.1142/S0219498818500871

On the integral and globally irreducible representations of finite groups

Dmitry Malinin

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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 OK of an algebraic number field K we are interested in the question: what are the conditions for subgroups G ⊂ GL(n,OK) such that OKG, the OK-span of G, coincides with M(n,OK), the ring of (n × n)-matrices over OK, and what are the minimal realization fields.

Original language	English
Article number	1850087
Journal	Journal of Algebra and its Applications
Volume	17
Issue number	5
DOIs	https://doi.org/10.1142/S0219498818500871
Publication status	Published - May 1 2018
Externally published	Yes

Keywords

Algebraic integers
Embedding problem
Finite groups
Globally irreducible representations
Schur ring
Steinitz class

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1142/S0219498818500871

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KW - Schur ring

KW - Steinitz class

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On the integral and globally irreducible representations of finite groups

Abstract

Keywords

ASJC Scopus subject areas

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