论文标题
Sylow $ 2 $ -SUBGROUP中的一组正常化链，以$ 2^n $字母为单位
A Chain of Normalizers in the Sylow $2$-subgroups of the symmetric group on $2^n$ letters
论文作者
论文摘要
在对称密码学的最初兴趣的基础上，在当前的工作中，我们研究了一组亚组。从Sylow $ 2 $ -Subgroup的AGL（2，N）开始，链条的每个术语都定义为对称组中前一个的标准制，以$ 2^n $字母。部分结果和计算实验使我们猜想，对于$ n $的巨大值，连续一个标准器的索引不取决于$ n $。确实，有充分的证据表明，这种索引的对数的顺序是将至少两个不同部分的分区数量的部分总和之一。
On the basis of an initial interest in symmetric cryptography, in the present work we study a chain of subgroups. Starting from a Sylow $2$-subgroup of AGL(2,n), each term of the chain is defined as the normalizer of the previous one in the symmetric group on $2^n$ letters. Partial results and computational experiments lead us to conjecture that, for large values of $n$, the index of a normalizer in the consecutive one does not depend on $n$. Indeed, there is a strong evidence that the sequence of the logarithms of such indices is the one of the partial sums of the numbers of partitions into at least two distinct parts.
