Sylow theory and the nilpotency class of left nilpotent skew braces

2026/06/24 by Gülin Ercan, Şükran Gül, İsmail Ş. Güloğlu +1
#math.GR

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Abstract

Let X be a finite left nilpotent skew brace and let π be a set of primes. We show that every Hall π-subgroup of the multiplicative group (X,⋅) is a Hall π-subbrace of X. This extends \cite[Theorem 11]CDDFT by removing the solvability assumption. As an application, we obtain an upper bound for the left nilpotency class of X in terms of the left nilpotency classes of its Sylow p-subbraces for every prime p dividing the order of X. We also show that every p-subbrace of X is contained in some Sylow p-subbrace.

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