Realisierbarkeit von Darstellungen endlicher Gruppen in Einheitswurzelkörpern. (Realizability of representations of finite groups in cyclotomic fields) (Q909778)

The content of this paper is described in the author's summary: ``Let D: \(G\to GL(n,{\mathbb{C}})\) be an irreducible linear representation of a finite group G with the character \(\chi\). If D is realizable in \({\mathbb{Q}}(\xi_ m)\) and \({\mathbb{Q}}(\xi_{m'})\) we give a condition for the realizability of D in \({\mathbb{Q}}(\xi_{(m,m')})\). If the degree n is a prime \(\neq 2\), we show that D is realizable in \({\mathbb{Q}}(\xi_ f)\), where f is the conductor of the abelian extension \({\mathbb{Q}}(\chi)/{\mathbb{Q}}.''\) The problem was motivated by certain questions in the theory of Galois representations.