识别自由群梯形子群的算法

IF 0.5 2区数学 Q3 MATHEMATICS International Journal of Algebra and Computation Pub Date : 2024-04-30 DOI:10.1142/s021819672450019x

Dario Ascari

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引用次数: 0

摘要

我们提供了一种算法，只要给定有限生成的自由群 F 的子群 H 的有限生成子集，就能确定 H 是否为梯形，如果答案是肯定的，还能计算出 H 为梯形的基。这就回答了罗森曼的一个问题。我们还通过一个反例证明了两个梯形子群的交集不一定是梯形，从而回答了罗森曼的另一个问题。

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An algorithm to recognize echelon subgroups of a free group

We provide an algorithm that, given a finite set of generators for a subgroup $H$ of a finitely generated free group $F$ , determines whether $H$ is echelon or not and, in case of affirmative answer, also computes a basis with respect to which $H$ is in echelon form. This gives an answer to a question of Rosenmann. We also prove, by means of a counterexample, that intersection of two echelon subgroups needs not to be echelon, answering another question of Rosenmann.

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来源期刊

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.

期刊最新文献

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