A generalization of strongly monomial groups.

Abstract Olivieri, del Río and Simón defined strongly monomial groups and a significant result proved by them is the explicit description of the simple components of the rational group algebra Q G of a strongly monomial group G. In this paper, generalized strongly monomial groups are defined, which is a generalization of strongly monomial groups. Beside strongly monomial groups, an extensive list of important families of groups which are generalized strongly monomial is produced. A description of the simple components of Q G , when G is a generalized strongly monomial group, is also provided. Furthermore, the work by Jespers, Olteanu, del Río and Van Gelder on the construction of a subgroup of finite index in the group of central units of integral group ring of a strongly monomial group has also been generalized. [ABSTRACT FROM AUTHOR]