与第二时空扬科群的自变群同谱的有限群的不可解性

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2023-12-28 DOI:10.1007/s10469-023-09723-0

A. Kh. Zhurtov, D. V. Lytkina, V. D. Mazurov

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引用次数: 0

摘要

对于有限群 G 而言，谱是群 G 的元素阶集合 ω(G)。G 的谱在可分性下是闭合的，因此由 ω(G)中可分性最大的元素组成的集合 μ(G) 唯一决定。我们证明与 Aut(J2) 等谱的有限群是不可解的。

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Unsolvability of Finite Groups Isospectral to the Automorphism Group of the Second Sporadic Janko Group

For a finite group G, the spectrum is the set ω(G) of element orders of the group G. The spectrum of G is closed under divisibility and is therefore uniquely determined by the set μ(G) consisting of elements of ω(G) that are maximal with respect to divisibility. We prove that a finite group isospectral to Aut(J₂) is unsolvable.

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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.