Construction of units in group rings of monomial and symmetric groups (Q1178934)

This paper may be thought as a continuation of the authors' article [Trans. Am. Math. Soc. 324, 603-621 (1991; Zbl 0723.16016)] and some other recent articles such as \textit{E. Jespers} and \textit{G. Leal} [Commun. Algebra 19, 1809-1827 (1991; Zbl 0723.16015)]. The main results permit the construction of subgroups of finite index in \(U(RG)\) for the case when \(R\) is a ring of cyclotomic integers and for a family of groups \(G\) which includes the monomial groups. This is accomplished by introducing natural generalizations of the Bass cyclic and bicyclic units, and also of some other families of units. Not very surprisingly, contexts of algebraic \(K\)-theory begin being used, but at present the works are highly technical and, in some cases (see, for example, theorems 3 and 4 dealing with the symmetric groups and some special metacyclic or metabelian groups), it is adapted to very particular cases. The paper is well written and clear but, apparently, there are a few typographical errors which may prejudicate the flow of easy lecture.