University of IsfahanInternational Journal of Group Theory2251-76507320180901On some integral representations of groups and global irreducibility81942228910.22108/ijgt.2017.100688.1402ENDmitryMalininUWI, Mona, KingstonJournal Article20161130Arithmetic 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 $GL(2,O_K)$.https://ijgt.ui.ac.ir/article_22289_b241fb85a1db50082f5c3c1e8b74e634.pdf