从铃木群体的自然表现中识别它们
Recognising the Suzuki groups in their natural representations
摘要：
在一个猜想的假设下，我们给出了Suzuki群Sz（q）（其中q = 2^{2 m + 1}，m > 0）在其4阶自然表示中的构造性成员检验的一个有效算法.它是一个Las Vegas算法，运行时间为O{log（q）}场操作，预处理步骤运行时间为O{log（q）loglog（q）}场操作。后一步需要求解GF（q）中的离散对数问题的预言机。我们还提出了一个识别算法Sz（q）=<X>。这是一个Las Vegas算法，运行时间为O{ |X| ^2}场运算。最后，我们给出了一个Las Vegas算法，对于<X>GL（4，q）中的某个h，给定^h = Sz（q），找到某个g，使得<X>^g = Sz（q）。运行时间为O{log（q）loglog（q）+ |X| }字段操作。该算法的实现可用于计算机系统MAGMA。
英文摘要：
Under the assumption of a certain conjecture, for which there exists strong experimental evidence, we produce an efficient algorithm for constructive membership testing in the Suzuki groups Sz(q), where q = 2^{2m + 1} for some m > 0, in their natural representations of degree 4. It is a Las Vegas algorithm with running time O{log(q)} field operations, and a preprocessing step with running time O{log(q) loglog(q)} field operations. The latter step needs an oracle for the discrete logarithm problem in GF(q). We also produce a recognition algorithm for Sz(q) = <X>. This is a Las Vegas algorithm with running time O{|X|^2} field operations. Finally, we give a Las Vegas algorithm that, given <X>^h = Sz(q) for some h in GL(4, q), finds some g such that <X>^g = Sz(q). The running time is O{log(q) loglog(q) + |X|} field operations. Implementations of the algorithms are available for the computer system MAGMA.
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。
