6 papers
Bidihedral skew braces
Alan Koch, Paul J. Truman
We classify skew braces with additive and multiplicative groups both isomorphic to the dihedral group . As a consequence, we obtain an alternative proof of the classificat…
Analogues of Sylow's first theorem, Cauchy's theorem, and Hall's theorem for skew braces
Paul J. Truman
We establish an unconditional analogue of Sylow's first theorem for finite skew braces, and deduce an analogue of Cauchy's theorem. We also prove an analogue of the existence part…
Bicyclic biskew braces
Hal Simpson, Paul J. Truman
We study finite braces whose additive and multiplicative groups are both cyclic. We reinterpret the classification of these braces from the perspective of regular subgroups of perm…
On some semidirect products of skew braces arising in Hopf-Galois theory
Paul J. Truman
We classify skew braces that are the semidirect product of an ideal and a left ideal. As a consequence, given a Galois extension of fields whose Galois group is the semidir…
Skew bracoids containing a skew brace
Ilaria Colazzo, Alan Koch, Isabel Martin-Lyons +1
Skew bracoids have been shown to have applications in Hopf-Galois theory. We show that a certain family of skew bracoids correspond bijectively with left cancellative semibraces. A…
Constructing skew bracoids via abelian maps, and solutions to the {Y}ang-{B}axter equation
Alan Koch, Paul J. Truman
We show how one can use the skew braces constructed using abelian maps to generate families of skew bracoids as defined by Martin-Lyons and Truman. Under certain circumstances, the…