Splitting of Normalizers of Maximal Tori in Finite Groups of Lie Type

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-01-05 DOI:10.1007/s10469-023-09721-2

A. A. Galt, A. M. Staroletov

引用次数: 0

Abstract

Let G be a finite group of Lie type, and T some maximal torus of the group G. We bring to a close the study of the question of whether there exists a complement for a torus T in its algebraic normalizer N (G, T). It is proved that any maximal torus of a group G ∈ {G₂(q), ²G₂(q), ³D₄(q)} has a complement in its algebraic normalizer. Also we consider the remaining twisted classical groups ²A_n(q) and ²D_n(q).

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列型有限群中最大环的归一化分裂

让 G 是一个有限的李型群，T 是群 G 的某个最大环。我们将结束对一个环 T 在其代数归一化 N (G, T) 中是否存在补集问题的研究。研究证明，群 G∈{G2(q), 2G2(q), 3D4(q)} 的任何最大环在其代数归一化中都有一个补集。此外，我们还考虑了其余的扭曲经典群 2An(q) 和 2Dn(q)。

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.