A chain of normalizers in the sylow 2 -subgroups of the symmetric group on 2^n letters

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 coincides with the sequence of the partial sums of the numbers of partitions into at least two distinct parts.