From the 1 of 14 linked papers with an AI index.
14 papers
Ideals and Solvability in Skew Braces
Marco Damele, Gülin Ercan
We investigate how nilpotency assumptions on the multiplicative group of a finite skew brace constrain its ideal structure and solvability. Our first main result shows that, if \(B…
Simple Skew Braces with Cyclic Sylow Subgroups
Marco Damele
We study simplicity and splitting phenomena in finite skew braces under cyclicity assumptions on Sylow subgroups. We first classify finite simple skew braces whose multiplicative g…
A Schur--Zassenhaus Theorem for Finite Skew Braces
Marco Damele
The paper proves a Schur–Zassenhaus type result for finite skew braces, showing that any ideal whose order is coprime to the order of the quotient brace has a complement.
On Simply Connected Simple Lie Skew Braces with Nilpotent Multiplicative Group
Marco Damele, Andrea Loi
We prove that a simply connected simple Lie skew brace with nilpotent multiplicative Lie group must be one-dimensional and abelian. Equivalently, if is a simply c…
A rigidity theorem for skew braces with multiplicative group \(S\times T\)
Marco Damele
We prove that if \(B\) is a finite skew brace with \((B,\cdot)\cong S\times T\), where \(S\) and \(T\) are non-abelian simple groups, then \((B,+)\) is not supersolvable.
On finite perfect two-sided skew braces
Marco Damele
We prove a structure theorem for finite perfect two-sided skew braces. The main tool is a central product theory for skew braces, developed here in both external and internal form;…