GDL

Journal from gdlhub / 2022-02-16 15:44:47
By : N. Ajmal, I. Jahan & B. Davvaz, Fuzzy Information and Engineering
Created : 2022-02-16, with 0 files

Keyword : L-algebra, L-subgroup, generated L-subgroup, normal L-subgroup, nilpotent L-subgroup
Url : http://www.tandfonline.com/doi/full/10.1080/16168658.2021.1997444
Document Source : web

This paper is in continuation of our previous works. In this paper, we study solvable L-subgroups of an L-group and establish a level subset characterisation for the same. Then, this level subset characterisation has been used to describe solvability of L-subgroups with the help of the notions of normal and subinvariant series of L-subgroups. Moreover, the concept of supersolvable L-subgroups of an L-group has been introduced. It has been established that supersolvable L-groups are closed under the formation of subgroups. Also, commutator L-subgroup of a supersolvable L-subgroup is shown to be nilpotent. In the last, we extend Zassenhaus Lemma to L-setting and utilise it to establish a version of Schreier Refinement Theorem in L-group Theory.

Description Alternative :

This paper is in continuation of our previous works. In this paper, we study solvable L-subgroups of an L-group and establish a level subset characterisation for the same. Then, this level subset characterisation has been used to describe solvability of L-subgroups with the help of the notions of normal and subinvariant series of L-subgroups. Moreover, the concept of supersolvable L-subgroups of an L-group has been introduced. It has been established that supersolvable L-groups are closed under the formation of subgroups. Also, commutator L-subgroup of a supersolvable L-subgroup is shown to be nilpotent. In the last, we extend Zassenhaus Lemma to L-setting and utilise it to establish a version of Schreier Refinement Theorem in L-group Theory.

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