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.

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
2021

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 coincides with the sequence of the partial sums of the numbers of partitions into at least two distinct parts.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/153130
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