17 papers
Classification of finite left-simple skew braces
Marco Damele
We give a complete classification of finite left-simple skew braces. We prove that a non-trivial finite skew brace has no non-trivial proper left ideals if and only if it is either…
Inverse Baer deformations and finite simple skew braces of nilpotent type
Marco Damele
Finite simple skew braces with non-abelian additive group remain largely unexplored. In particular, to the best of our knowledge, no finite simple skew brace with non-abelian nilpo…
Kernel--wreath constructions and infinite families of finite simple skew braces
Marco Damele
We introduce a kernel--wreath construction for finite skew braces. Let be a finite skew brace, write and , and let be an epimor…
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
We prove a Schur--Zassenhaus theorem for finite skew braces. More precisely, if \(B\) is a finite skew brace and \(I\) is an ideal of \(B\) such that \(|I|\) and \(|B/I|\) are copr…
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…
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;…
Solvability and Rigidity for Topological Skew Braces
Marco Damele, Andrea Loi
We study compact and locally compact topological analogues of the Byott--Vendramin solvability problem for finite skew braces, asking whether solvability of the additive group forc…
On simple compact Lie skew braces
Marco Damele, Andrea Loi
We study simplicity of Lie skew braces from both global and infinitesimal perspectives. After reviewing the correspondence between connected Lie skew braces, simply transitive affi…
On the multiplicative group of a two-sided skew brace of solvable type
Marco Damele
We prove that if is a two-sided skew brace whose additive group is solvable, then every finite quotient of the multiplicative group is solvable. In partic…
Finite skew braces whose additive group is a Z-group
Marco Damele
Rump proved in \cite[Theorem~1]{Rump2018ClassificationOC} that if a finite skew brace has cyclic additive group, then its multiplicative group is solvable and almost Sylow cyclic.…
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 a Cauchy theorem for finite skew braces
Marco Damele, Vicent Pérez Calabuig
One of the major problems in the structural theory of skew braces consists in the classification of skew braces of finite order up to isomorphism. In this light, the open question…
Galois' Professor's Revenge
M. Damele, A. Loi, M. Mereb +1
We prove that the groups associated with the Revenge Cube and the Professor's Cube can be realized as Galois groups over the rationals.
Finite groups in which every proper characteristic subgroup is cyclic
Marco Damele, Fabio Mastrogiacomo
Let be a finite non-cyclic, non-characteristically simple group with the property that all proper characteristic subgroups of are cyclic. We call such a group $\mathrm{CCS}…
Structural and rigidity properties of Lie skew braces
Marco Damele, Andrea Loi
We investigate structural and rigidity properties of \emph{Lie skew braces} (LSBs), objects essentially known in the literature as \emph{post--Lie groups}, obtained by endowing a m…