A generalization of strongly monomial groups

TL;DR

This paper introduces generalized strongly monomial groups, extending the class of strongly monomial groups, and provides descriptions of their rational group algebra components along with related subgroup constructions.

Contribution

It defines generalized strongly monomial groups, broadens the class of groups with known algebraic properties, and generalizes existing subgroup construction results.

Findings

Extended the class of strongly monomial groups to generalized strongly monomial groups.

Provided explicit descriptions of simple components of $\

Generalized subgroup constructions for the group of central units in integral group rings.

Abstract

Olivieri, del R{\'{\i}}o and Sim{\'o}n defined strongly monomial groups and a significant result proved by them is the explicit description of the simple components of the rational group algebra $\mathbb{Q}G$ 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 $\mathbb{Q}G$, when $G$ is a generalized strongly monomial group, is also provided. Furthermore, the work by Jespers, Olteanu, del R{\'{\i}}o 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.