Modularity of the Lattice of Baer n-Multiply σ-Local Formations

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-08-13 DOI:10.1007/s10469-024-09747-0

N. N. Vorob’ev

引用次数: 0

Abstract

Let σ be a partition of the set of all prime numbers into a union of pairwise disjoint subsets. Using the idea of multiple localization due to A. N. Skiba, we introduce the notion of a Baer n-multiply σ-local formation of finite groups. It is proved that with respect to inclusion ⊆, the collection of all such formations form a complete algebraic modular lattice. Thereby we generalize the result obtained by A. N. Skiba and L. A. Shemetkov in [Ukr. Math. J., 52, No. 6, 783-797 (2000)].

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Baer n乘σ局部网格的模块性

设 σ 是将所有素数集合划分为一对互不相交的子集的联合。利用 A. N. Skiba 提出的多重局部化思想，我们引入了有限群的 Baer n 多重 σ 局部形成的概念。我们证明，就包含⊆而言，所有此类形成的集合构成了一个完整的代数模格网。因此，我们推广了 A. N. Skiba 和 L. A. Shemetkov 在 [乌克兰数学学报，52，第 6 期，783-797 (2000)]中获得的结果。

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

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.