4 citations · 6 across the 6 of their papers we have counts for
13 papers
Non-involutive solutions of the Yang-Baxter equation of multipermutation level 2
Jan Hora, Premysl Jedlicka, Agata Pilitowska
We study non-degenerate set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2 which are not 2-reductive. We describe an effective way of constructing such…
Diagonals of solutions of the Yang-Baxter equation
Premysl Jedlicka, Agata Pilitowska
We study the diagonal mappings in non-involutive set-theoretic solutions of the Yang-Baxter equation. We show that, for non-degenerate solutions, they are commuting bijections. Thi…
Skew left braces and 2-reductive solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska
We study 2-reductive non-involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation. We give a combinatorial construction of any such solution of any (even infin…
Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We present a construction of all finite indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level at most 2 with abelian permutation group. As a c…
Homomorphic images of affine quandles
Přemysl Jedlička, David Stanovský
We are interested in abstract conditions that characterize homomorphic images of affine quandles. Our main result is a two-fold characterization of this class: one by a property of…
Subquandles of affine quandles
Přemysl Jedlička, Agata Pilitowska, David Stanovský +1
A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their d…
Distributive and trimedial quasigroups of order 243
Přemysl Jedlička, David Stanovský, Petr Vojtěchovský
We enumerate three classes of non-medial quasigroups of order up to isomorphism. There are non-medial trimedial quasigroups of order (extending the work of…
Free medial quandles
Premysl Jedlicka, Agata Pilitowska, Anna Zamojska-Dzienio
This paper brings the construction of free medial quandles as well as free -symmetric medial quandles and free -reductive medial quandles.
Subdirectly irreducible medial quandles
Premysl Jedlicka, Agata Pilitowska, Anna Zamojska-Dzienio
We describe all subdirectly irreducible medial quandles. We show that they fall within one of four disjoint classes. In particular, in the finite case they are either connected (an…
The structure of medial quandles
Přemysl Jedlička, Agata Pilitowska, David Stanovský +1
Medial quandles are represented using a heterogeneous affine structure. As a consequence, we obtain numerous structural properties, including enumeration of isomorphism classes of…
Nilpotency in automorphic loops of prime power order
Premysl Jedlicka, Michael Kinyon, Petr Vojtechovsky
A loop is automorphic if its inner mappings are automorphisms. Using so-called associated operations, we show that every commutative automorphic loop of odd prime power order is ce…
Constructions of commutative automorphic loops
Premysl Jedlicka, Michael Kinyon, Petr Vojtechovsky
A loop whose inner mappings are automorphisms is an \emph{automorphic loop} (or \emph{A-loop}). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the i…
The Structure of Commutative Automorphic Loops
Premysl Jedlicka, Michael Kinyon, Petr Vojtechovsky
An \emph{automorphic loop} (or \emph{A-loop}) is a loop whose inner mappings are automorphisms. Every element of a commutative A-loop generates a group, and $(xy)^{-1} = x^{-1}y^{-…