On some integral representations of groups and global irreducibility.

On some integral representations of groups and global irreducibility.

Blog Article

Arithmetic aspects of integral representations of finite groups and their irreducibility are considered with a focus on globally irreducible representations and their generalizations to Electrolytic 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 photo frame to a subgroup of $GL(2,O_K)$.