Finite skew braces satisfy Schur-Zassenhaus for Hall ideals with complements and Sylow's third theorem on the count of Sylow p-sub-skew braces, with counterexamples for arbitrary sub-skew braces.
On the Sylow Theorem for Skew Braces
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
We discuss the (first) Sylow theorem for certain classes of finite skew braces, proving it to hold true when the skew brace is two-sided, bi-skew, right nilpotent, $\lambda$-homomorphic or supersoluble. We also show it to hold true for soluble skew braces that are left-nilpotent, and address a number of more specialized settings, proving general Hall-type theorems.
fields
math.GR 4years
2026 4representative citing papers
Every ideal of coprime order in a finite skew brace admits a complement that is a sub-skew brace.
Analogues of Sylow's first, Cauchy's, and Hall's theorems are established for finite skew braces, with application to classification of order pq examples.
For finite left nilpotent skew braces, multiplicative Sylow p-subgroups are always Sylow p-subbraces, removing the solvability assumption from prior work.
citing papers explorer
-
The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces
Finite skew braces satisfy Schur-Zassenhaus for Hall ideals with complements and Sylow's third theorem on the count of Sylow p-sub-skew braces, with counterexamples for arbitrary sub-skew braces.
-
A Schur--Zassenhaus Theorem for Finite Skew Braces
Every ideal of coprime order in a finite skew brace admits a complement that is a sub-skew brace.
-
Analogues of Sylow's first theorem, Cauchy's theorem, and Hall's theorem for skew braces
Analogues of Sylow's first, Cauchy's, and Hall's theorems are established for finite skew braces, with application to classification of order pq examples.
-
Sylow theory and the nilpotency class of left nilpotent skew braces
For finite left nilpotent skew braces, multiplicative Sylow p-subgroups are always Sylow p-subbraces, removing the solvability assumption from prior work.