On some integral representations of groups and global irreducibility.

On some integral representations of groups and global irreducibility.

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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 ranch style beans shirt are discussed.Let $K$ be a finite extension persol 3195 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 $GL(2,O_K)$.