Solvability, Supersolvability and Schreier Refinement Theorem for L-Subgroups

IF 1.3 Q2 MATHEMATICS, APPLIED
N. Ajmal, I. Jahan, B. Davvaz
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引用次数: 1

Abstract

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.
l -子群的可解性、超可解性及Schreier细化定理
这篇论文是我们以前工作的延续。本文研究了一类l群的可解l子群,并建立了它们的水平子集刻画。然后,借助l -子群的正规级数和次不变级数的概念,利用这一水平子集特征描述了l -子群的可解性。此外,还引入了l群的超可解l子群的概念。证明了超可解l群在子群的形成下是封闭的。此外,还证明了超可解l子群的对易子l子群是幂零的。最后,我们将Zassenhaus引理推广到l集合,并利用它建立了l群理论中Schreier精化定理的一个版本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
13
审稿时长
40 weeks
期刊介绍: Fuzzy Information and Engineering—An International Journal wants to provide a unified communication platform for researchers in a wide area of topics from pure and applied mathematics, computer science, engineering, and other related fields. While also accepting fundamental work, the journal focuses on applications. Research papers, short communications, and reviews are welcome. Technical topics within the scope include: (1) Fuzzy Information a. Fuzzy information theory and information systems b. Fuzzy clustering and classification c. Fuzzy information processing d. Hardware and software co-design e. Fuzzy computer f. Fuzzy database and data mining g. Fuzzy image processing and pattern recognition h. Fuzzy information granulation i. Knowledge acquisition and representation in fuzzy information (2) Fuzzy Sets and Systems a. Fuzzy sets b. Fuzzy analysis c. Fuzzy topology and fuzzy mapping d. Fuzzy equation e. Fuzzy programming and optimal f. Fuzzy probability and statistic g. Fuzzy logic and algebra h. General systems i. Fuzzy socioeconomic system j. Fuzzy decision support system k. Fuzzy expert system (3) Soft Computing a. Soft computing theory and foundation b. Nerve cell algorithms c. Genetic algorithms d. Fuzzy approximation algorithms e. Computing with words and Quantum computation (4) Fuzzy Engineering a. Fuzzy control b. Fuzzy system engineering c. Fuzzy knowledge engineering d. Fuzzy management engineering e. Fuzzy design f. Fuzzy industrial engineering g. Fuzzy system modeling (5) Fuzzy Operations Research [...] (6) Artificial Intelligence [...] (7) Others [...]
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