Connecting monomiality questions with the structure of rational group algebras
| Autor: | Gurleen Kaur, Gurmeet K. Bakshi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Class (set theory) Monomial Algebra and Number Theory Mathematics::Commutative Algebra Primary 16S34 20C15 Secondary 20C05 Generalization Group (mathematics) Algebraic structure Rational group Structure (category theory) Mathematics - Rings and Algebras Rings and Algebras (math.RA) FOS: Mathematics Mathematics |
| Popis: | In recent times, there has been a lot of active research on monomial groups in two different directions. While group theorists are interested in the study of their normal subgroups and Hall subgroups, the interest of group ring theorists lie in the structure of their rational group algebras due to varied applications. The purpose of this paper is to bind the two threads together. Revisiting Dade's celebrated embedding theorem which states that a finite solvable group can be embedded inside some monomial group, it is proved here that the embedding is indeed done inside some generalized strongly monomial group. The so called generalized strongly monomial groups arose in a recent work of authors while understanding the algebraic structure of rational group algebras. Still unresolved monomiality questions have been correlated by proving that all the classes of monomial groups where they have been answered are generalized strongly monomial. The study also raises some intriguing questions weaker than those asked by Dornhoff and Isaacs in their investigations. |
| Databáze: | OpenAIRE |
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