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 QG 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 QG, 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.

Structure of group rings and the group of units of integral group rings: an invitation

“…Recently, a beautiful generalization of this result has been obtained by Bakshi and Kaur [4] for a uch wider class of groups, the class consisting of the generalized strongly monomial groups (which defined via the notion of generalized strong Shoda pair).…”

“…In [4] Bakshi and Kaur introduced the class of generalized strongly monomial groups. This is based on generalized strong Shoda pairs of a finite group and leads to the class generalized strongly monomial groups.…”