%0 Journal Article
%T On some integral representations of groups and global irreducibility
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Malinin, Dmitry
%D 2018
%\ 09/01/2018
%V 7
%N 3
%P 81-94
%! On some integral representations of groups and global irreducibility
%K globally irreducible representations
%K class numbers
%K genera
%K Hilbert symbol
%K torsion points of elliptic curves
%R 10.22108/ijgt.2017.100688.1402
%X 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 $GL(2,O_K)$.
%U https://ijgt.ui.ac.ir/article_22289_b241fb85a1db50082f5c3c1e8b74e634.pdf