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。
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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