2020/10/27 by Gurmeet K. Bakshi, Bakshi, Gurmeet K., Gurleen Kaur +1
Computer Science · Mathematics · #20C15 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Primary 16S34 #Rings and Algebras (math.RA) #Secondary 20C05 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2010.14203
openalex publication_date 2020/10/27 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In recent times, there has been a lot of active research on monomial groups\nin two different directions. While group theorists are interested in the study\nof their normal subgroups and Hall subgroups, the interest of group ring\ntheorists lie in the structure of their rational group algebras due to varied\napplications. The purpose of this paper is to bind the two threads together.\nRevisiting Dade's celebrated embedding theorem which states that a finite\nsolvable group can be embedded inside some monomial group, it is proved here\nthat the embedding is indeed done inside some generalized strongly monomial\ngroup. The so called generalized strongly monomial groups arose in a recent\nwork of authors while understanding the algebraic structure of rational group\nalgebras. Still unresolved monomiality questions have been correlated by\nproving that all the classes of monomial groups where they have been answered\nare generalized strongly monomial. The study also raises some intriguing\nquestions weaker than those asked by Dornhoff and Isaacs in their\ninvestigations.\n