on some integral representations of groups and global irreducibility.

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 ok the ring of integers of k. let g be a finite subgroup of gl(2,k), the group of (2×2)-matrices over k. we obtain some conditions on k for g to be conjugate to a subgroup of gl(2,ok).