  We restrict the type of $2 \times 2$-matrices which can occur as simple
components in the Wedderburn decomposition of the rational group algebra of a
finite group. This results in a description up to commensurability of the group
of units of the integral group ring $\mathbb Z G$ for all finite groups $G$
that do not have a non-commutative Frobenius complement as a quotient.

Group Theory