3 papers
math.GR2026
The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces
M. Ferrara, M. Trombetti
In this short note we establish the Schur--Zassenhaus Theorem and Sylow's Third Theorem for finite skew braces. More precisely, we prove that every Hall ideal of a finite skew brac…
math.GR2025
The Pseudocentre of a Group (with an appendix by Anthony Genevois)
Mattia Brescia, Bernardo Giuseppe Di Siena, Ernesto Ingross +1
In 1973, Jim Wiegold introduced the concept of pseudocentre P(G) of a group G as the intersection of the normal closures of the centralizers of its elements. He proved that the pse…
math.RA2025
On Dedekind Skew Braces
A. Caranti, I. Del Corso, M. Di Matteo +2
Skew braces play a central role in the theory of set-theoretic non-degenerate solutions of the Yang--Baxter equation, since their algebraic properties significantly affect the beha…