5 citations · 17 across the 14 of their papers we have counts for
9 papers · 1 filter
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…
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…
Skew bracoids
Isabel Martin-Lyons, Paul J. Truman
Skew braces are intensively studied owing to their wide ranging connections and applications. We generalize the definition of a skew brace to give a new algebraic object, which we…
Abelian fixed point free endomorphisms and the Yang-Baxter equation
Alan Koch, Laura Stordy, Paul J. Truman
We obtain a simple family of solutions to the set-theoretic Yang-Baxter equation, one which depends only on considering special endomorphisms of a finite group. We show how such an…
Skew left braces and isomorphism problems for Hopf-Galois structures on Galois extensions
Alan Koch, Paul J. Truman
Given a finite group , we study certain regular subgroups of the group of permutations of , which occur in the classification theories of two types of algebraic objects:…
Opposite skew left braces and applications
Alan Koch, Paul J. Truman
Given a skew left brace , we introduce the notion of an "opposite" skew left brace , which is closely related to the concept of the opposite of a group…