A Subnormality Criterion in Finite Groups Related to Character Degrees

Riese, Udo

doi:10.1006/jabr.1997.7259

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Generalized Strongly Monomial Groups1

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1998

2022

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Cited by 5 publications

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“…(v) Suppose χ is an irreducible character of G induced from a linear character of an abelian subgroup, say A. Then Theorem A of [23] yields that A must be subnormal in G. Consequently, G is subnormally monomial.…”

Section: Generalized Strongly Monomial Groupsmentioning

confidence: 99%

A generalization of strongly monomial groups

Bakshi

Kaur

2019

Journal of Algebra

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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.

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Section: Generalized Strongly Monomial Groupsmentioning

confidence: 99%