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arXiv · 2008.13423

A Chain of Normalizers in the Sylow $2$-subgroups of the symmetric group on $2^n$ letters

Riccardo Aragona·Roberto Civino·Norberto Gavioli·Carlo Maria Scoppola
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Abstract

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.

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Riccardo Aragona, Roberto Civino, Norberto Gavioli, Carlo Maria Scoppola. 2020-08-31. A Chain of Normalizers in the Sylow $2$-subgroups of the symmetric group on $2^n$ letters. https://doi.org/10.1007/s13226-021-00190-w

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