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Corpus ID: 221376346

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

@article{Aragona2020ACO,
title={A Chain of Normalizers in the Sylow \$2\$-subgroups of the symmetric group on \$2^n\$ letters},
author={R. Aragona and Roberto Civino and N. Gavioli and C. Scoppola},
journal={arXiv: Group Theory},
year={2020}
}

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… Expand