Large subgroups in the unit groups of arithmetic orders (Q1906634)

This interesting and well written paper deals with the problem of effectively constructing a finite index subgroup of the units group of an order in a semisimple \(k\)-algebra \(A\), where \(k\) is a local or global algebraic number field. For the ``effectiveness'' of the construction (whose meaning is precisely described in the article) it is used that \(A\) is given as a product of cyclic crossed product algebras. It should be said that the methods designed here do not apply to some few exceptions. This construction is of interest for applications to recent developments in the study of unit groups of group rings [see \textit{E. Jespers} and \textit{G. Leal}, Manuscr. Math. 78, No. 3, 303-315 (1993; Zbl 0802.16025)] and, also, in algebraic number theory.