A Functorial Generalization of the Fitting Subgroup in Finite Groups

IF 0.4 3区数学 Q4 LOGIC Algebra and Logic Pub Date : 2024-09-27 DOI:10.1007/s10469-024-09754-1

V. I. Murashko, A. F. Vasil’ev

引用次数: 0

Abstract

Using the functional approach of R. Baer and B. I. Plotkin, we introduce and study the notion of ℱ-functorial whose values are characteristic subgroups of a finite group that possess certain properties of the Fitting subgroup. The lattice and semigroups of ℱ-functorials are described, the interrelation between ℱ-functorials and classes of groups is established, a characterization of their values is given in terms of group’s elements inducing inner automorphisms on specified chief factors.

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有限群中拟合子群的赋形泛化

利用 R. Baer 和 B. I. Plotkin 的函数方法，我们引入并研究了ℱ-矢量的概念。普洛特金的方法，我们引入并研究了ℱ-矢量的概念，它的值是有限群的特征子群，具有拟合子群的某些性质。我们描述了ℱ-矢量的晶格和半群，建立了ℱ-矢量和群类之间的相互关系，并根据在指定主因上诱导内自动形的群元给出了ℱ-矢量值的特征。

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.

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