Computing generators of free modules over orders in group algebras. (Q947499)

Let \(E\) be an algebraic number field with maximal order \(\mathcal O\), and let \(\Lambda\) be an \(\mathcal O\)-order in the group ring \(E[G]\) over a finite group \(G\). Under the assumption that the Schur indices of all \(E\)-rational irreducible characters of \(G\) are 1, the authors give a computationally useful criterion for \(\Lambda\)-lattices to be free of a given rank. An application to Galois modules is indicated.