TY - JOUR
ID - 22289
TI - On some integral representations of groups and global irreducibility
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Malinin, Dmitry
AD - UWI, Mona, Kingston
Y1 - 2018
PY - 2018
VL - 7
IS - 3
SP - 81
EP - 94
KW - globally irreducible representations
KW - class numbers
KW - genera
KW - Hilbert symbol
KW - torsion points of elliptic curves
DO - 10.22108/ijgt.2017.100688.1402
N2 - 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 $GL(2,O_K)$.
UR - https://ijgt.ui.ac.ir/article_22289.html
L1 - https://ijgt.ui.ac.ir/article_22289_b241fb85a1db50082f5c3c1e8b74e634.pdf
ER -