@article {
author = {Malinin, Dmitry},
title = {On some integral representations of groups and global irreducibility},
journal = {International Journal of Group Theory},
volume = {7},
number = {3},
pages = {81-94},
year = {2018},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2017.100688.1402},
abstract = {Arithmetic aspects of integral representations of finite groups and their irreducibility are considered with a focus on globally irreducible representations and their generalizations to arithmetic rings. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed. Let $K$ be a finite extension of the rational number field and $O_K$ the ring of integers of $K$. Let $G$ be a finite subgroup of $GL(2,K)$, the group of $(2 \times 2)$-matrices over $K$. We obtain some conditions on $K$ for $G$ to be conjugate to a subgroup of $GL(2,O_K)$.},
keywords = {globally irreducible representations,class numbers,genera,Hilbert symbol,torsion points of elliptic curves},
url = {https://ijgt.ui.ac.ir/article_22289.html},
eprint = {https://ijgt.ui.ac.ir/article_22289_b241fb85a1db50082f5c3c1e8b74e634.pdf}
}