On integral representations of 𝑝-solvable groups

Abstract

It is a long standing problem whether every irreducible representation of a finite group G G can be realized over the ring of integers Z [ μ g ] \mathbb Z[\mu _g] of the g = exp ⁡ ( G ) g=\exp (G) -cyclotomic field Q ( g ) \mathbb Q (g) . We present a result which combines and extends the previously known criteria.