Algebra Seminar by Norberto Gavioli

Charlotte Scott Centre for Algebra

On Wednesday the 10th of November 2021, Norberto Gavioli (Università degli Studi dell’Aquila) will be giving an online seminar on his research at 4.45pm. The details of his talk are as follows:

Title: A chain of normalizers in the Sylow 2-subgroup of Sym(2^n).

Abstract: The normalizer of a regular elementary abelian 2-subgroup in the symmetric group Sym(2^n) is the affine group AGL(2^n). Due to some questions arising from differential cryptanalysis of block cyphers, we started studying the normalizer chain in Sym(2^n) starting from the Sylow 2-subgroup of AGL(2^n). Computational results suggested a possible connection with the sequence (a_m) of the number of partitions of minto distinct parts already studied by Euler. We could prove indeed that for ile n-2 the the base 2 logarithm index of the i-th term of the chain in the (i-1)-th one is equal to (i-2)-th term of the partial sum sequence arising from (a_m). This…

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