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 |
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Article number | 1850087 |
Journal | Journal of Algebra and its Applications |
Volume | 17 |
Issue number | 5 |
DOIs | |
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