Development of <em>L</em>-Group Theory
In this work, we present a systematic and successful development of L-group theory. A universal construction of a generated L-subgroup has been provided by using level subsets of given L-subsets. This construction allows us to define and study commutator L-subgroups, normalizer of an L-subgroup, nil...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
| Publicado: |
IntechOpen
2023
|
| Materias: | |
| Acceso en línea: | https://www.intechopen.com/chapters/86874 |
| Etiquetas: |
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | In this work, we present a systematic and successful development of L-group theory. A universal construction of a generated L-subgroup has been provided by using level subsets of given L-subsets. This construction allows us to define and study commutator L-subgroups, normalizer of an L-subgroup, nilpotent L-subgroups, solvable L-subgroups, normal closure of an L-subgroup. All these concepts and their inter-relationships have been presented. Here we mention that in this work we also exhibit a characterization of solvable L-subgroup with the help of a series of L-subgroups such that at each level, the factor groups of level subgroups of their consecutive members are Abelian. This allows us to introduce the notion of a supersolvable L-subgroup by using the factors of level subgroups at each level of a subinvariant series of an L-subgroup. Also, by using successive normal closures, we transfinitely define a series called the normal closure series of the L-subgroup. It has been shown that it is the fastest descending normal series containing given L-subgroup. This sets the ground for the development of subnormality in L-group theory. In the last, we study the notion of subnormal L-subgroups. |
|---|---|
| ISBN: | 978-1-83768-529-5 |
| DOI: | 10.5772/intechopen.110387 |