无边群中的公共横截面和补集

Pub Date : 2024-02-24 DOI:10.1007/s10801-024-01299-x

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引用次数: 0

摘要

摘要给定一个有限无秩群 G 和 G 的同阶循环子群 A、B、C，我们发现 A、B、C 的余集有必要条件和充分条件。对于任意数量的循环子群，我们给出了存在共同补集的充分条件。此外，在存在共同横截面的几种情况下，我们提供了具体的构造。

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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Common transversals and complements in abelian groups

Abstract

Given a finite abelian group G and cyclic subgroups A, B, C of G of the same order, we find necessary and sufficient conditions for A, B, C to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions.

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