TRIPLE-PRODUCT-FREE集

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2023-10-06 DOI:10.1017/s0004972723000941

PRECIOUS U. AGIGOR-MIKE, SARAH B. HART, MARTIN C. OBI

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引用次数: 0

摘要

摘要本文研究了三积集，它类似于广泛研究的无积集的概念。如果群G的非空子集S对于S$中的所有$ A, b, c $是无三积的。如果S是无三积集合并且不是任何其他无三积集合的真子集，我们说S是局部极大的。我们对包含大小为1的局部极大无三积集的所有群进行分类。然后，我们得到了群的一个子集局部极大三积无的充要条件，并与标准三积集的情况作了一些观察和比较。

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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TRIPLE-PRODUCT-FREE SETS

Abstract In this paper, we study triple-product-free sets, which are analogous to the widely studied concept of product-free sets. A nonempty subset S of a group G is triple-product-free if $abc \notin S$ for all $a, b, c \in S$ . If S is triple-product-free and is not a proper subset of any other triple-product-free set, we say that S is locally maximal. We classify all groups containing a locally maximal triple-product-free set of size 1. We then derive necessary and sufficient conditions for a subset of a group to be locally maximal triple-product-free, and conclude with some observations and comparisons with the situation for standard product-free sets.

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society