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arXiv · 1805.00196

A generalization of strongly monomial groups

Gurmeet K. Bakshi·Gurleen Kaur
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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.

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Gurmeet K. Bakshi, Gurleen Kaur. 2018-05-01. A generalization of strongly monomial groups. https://arxiv.org/abs/1805.00196

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