Abstract:Let $X$ be a finite left nilpotent skew brace and let $p$ be a prime dividing $|X|$. We show that every Sylow $p$-subgroup of the multiplicative group $(X,\cdot)$ is a Sylow $p$-subbrace of $X$, and that every $p$-subbrace of $X$ is contained in some Sylow $p$-subbrace. This extends a recent result of Caranti, Del Corso, Di Matteo, Ferrara, and Trombetti 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.
From: Şükran Gül [view email]
[v1]
Wed, 24 Jun 2026 11:01:30 UTC (7 KB)
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