未知次数交错群的快速识别
Fast recognition of alternating groups of unknown degree
摘要：
我们提出了一个构造性的识别算法，以决定是否一个给定的黑盒群是同构的交替或对称群没有先验知识的程度。这消除了已知算法中的主要差距，因为它们需要度作为额外的输入。我们的方法是概率的，并依赖于结果的比例与某些性质的元素交替和对称群。这些结果是独立的利益，例如，我们建立了一个下界的比例对合小支持。
英文摘要：
We present a constructive recognition algorithm to decide whether a given black-box group is isomorphic to an alternating or a symmetric group without prior knowledge of the degree. This eliminates the major gap in known algorithms, as they require the degree as additional input. Our methods are probabilistic and rely on results about proportions of elements with certain properties in alternating and symmetric groups. These results are of independent interest; for instance, we establish a lower bound for the proportion of involutions with small support.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
