三阶共三次方有限毛方环中的同余可解性

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-07-15 DOI:10.1007/s00025-024-02231-2

Aleš Drápal, Petr Vojtěchovský

引用次数: 0

摘要

我们证明，当且仅当 \(u(x,y\in X\) 和 \(u\in Q\) 时，毛方环路 Q 的正常子环路 X 会诱导 Q 的无旁系同余。然后，我们利用这一特征来证明可经典求解的有限 3 分 Moufang 循环是可全等求解的。

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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Congruence Solvability in Finite Moufang Loops of Order Coprime to Three

We prove that a normal subloop X of a Moufang loop Q induces an abelian congruence of Q if and only if \(u(xy) = (uy)x\) for all \(x,y\in X\) and \(u\in Q\). This characterization is then used to show that classically solvable finite 3-divisible Moufang loops are congruence solvable.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.