On integral absolutely irreducible representations of finite groups. (Q2797003)

Let \(G\) be the finite \(p\)-group of order \(p^{3m}\) generated by 2 elements of order \(p^m\) whose commutator has also order \(p^m\). The paper gives explicit matrices for infinitely many absolutely irreducible representations of \(G\) of degree \(p^m\) over \(\mathbb Q_p[\zeta_{p^\infty}]\) and \(\mathbb Q[\zeta_{p^\infty}]\) that are pairwise inequivalent over the respective rings of integers. The author concludes that a similar result holds for arbitrary non abelian finite \(p\)-groups \(G\). The last section deals with integral representations of generalised quaternion groups.