铃木群的黑盒识别
Black Box Recognition of the Suzuki groups
AI总结：
研究铃木群$Sz(q)$的黑盒识别，提出构造标准生成元、进行构造性成员测试及给出高效验证表示的算法，且已在Magma中实现。
AI中文摘要：
我们提出一种黑盒算法，用以构造铃木群$Sz(q)$（其中$q = 2^{2m + 1}$，$m > 0$）的标准生成元。该算法是单边蒙特卡罗算法，无误报。还提出一种在$Sz(q)$中进行构造性成员测试的黑盒算法，并将元素写成标准生成元的直线程序。最后给出一个易于验证的$Sz(q)$表示。算法已在计算机代数系统Magma中实现。
英文摘要：
We present a black box algorithm that constructs standard generators for the Suzuki groups $Sz(q)$, where $q = 2^{2m+1}$ for some $m > 0$. The algorithm is one-sided Monte Carlo, with no false positives. We also present a black box algorithm that performs constructive membership testing in $Sz(q)$, and writes an element as a straight line program in the standard generators. Finally, we give a presentation for $Sz(q)$ that is efficient to verify. The algorithms have been implemented in the computer algebra system Magma.
