On the irreducible matrix representations of finite 2-groups over local factorial rings (Q2759400)

The authors prove that if \(G\) is a finite 2-group of order \(|G|>2\), \(K\) is a local factorial ring of characteristic zero with residue class field of characteristic 2, and 2 is a prime element of the ring \(K\), then any irreducible matrix \(K\)-representation of the group \(G\) is irreducible over the field of fractions \(F\) of the ring \(K\) if and only if \(K\) is a discretely normed ring.