Zobrazeno 1 - 10
of 241
pro vyhledávání: '"Vojtěchovský, Petr"'
Autor:
Drápal, Aleš, Vojtěchovský, Petr
We study abelian-by-cyclic Moufang loops. We construct all split $3$-divisible abelian-by-cyclic Moufang loops from so-called Moufang permutations on abelian groups $(X,+)$, which are permutations that deviate from an automorphism of $(X,+)$ by an al
Externí odkaz:
http://arxiv.org/abs/2301.03683
Autor:
Drápal, Aleš, Vojtěchovský, Petr
We prove that a normal subloop $X$ of a Moufang loop $Q$ induces an abelian congruence of $Q$ if and only if each inner mapping of $Q$ restricts to an automorphism of $X$ and $u(xy) = (uy)x$ for all $x,y\in X$ and $u\in Q$. The former condition can b
Externí odkaz:
http://arxiv.org/abs/2301.03680
Autor:
Drápal, Aleš, Vojtěchovský, Petr
In groups, an abelian normal subgroup induces an abelian congruence. We construct a class of centrally nilpotent Moufang loops containing an abelian normal subloop that does not induce an abelian congruence. On the other hand, we prove that in $6$-di
Externí odkaz:
http://arxiv.org/abs/2301.03646
Autor:
Stanovský, David, Vojtěchovský, Petr
We find a short equational basis for the variety of $3$-supernilpotent loops. We also present a conceptually simple proof that $k$-nilpotence and $k$-supernilpotence are equivalent for groups. Connections between $3$-supernilpotent loops, Moufang loo
Externí odkaz:
http://arxiv.org/abs/2209.08128
We describe, implement and test a novel method for training neural networks to estimate the Jacobian matrix $J$ of an unknown multivariate function $F$. The training set is constructed from finitely many pairs $(x,F(x))$ and it contains no explicit i
Externí odkaz:
http://arxiv.org/abs/2204.00523
A quandle is an algebraic structure satisfying three axioms: idempotency, right-invertibility and right self-distributivity. In quandles, right translations are permutations. The profile of a quandle is the list of cycle structures, one per right tra
Externí odkaz:
http://arxiv.org/abs/2104.10199
Autor:
Drápal, Aleš, Vojtěchovský, Petr
Publikováno v:
Aequationes mathematicae, volume 94 (2020), pages 97-101
A loop $X$ is said to satisfy Moufang's theorem if for every $x,y,z\in X$ such that $x(yz)=(xy)z$ the subloop generated by $x$, $y$, $z$ is a group. We prove that the variety $V$ of Steiner loops satisfying the identity $(xz)(((xy)z)(yz)) = ((xz)((xy
Externí odkaz:
http://arxiv.org/abs/2101.04000
Autor:
Drápal, Aleš, Vojtěchovský, Petr
Publikováno v:
Glasgow Mathematical Journal, Volume 62, Issue 3, September 2020, pp. 600-630
A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division sudokus wit
Externí odkaz:
http://arxiv.org/abs/2101.03995
Autor:
Stanovský, David, Vojtěchovský, Petr
Idempotent left nondegenerate solutions of the Yang-Baxter equation are in one-to-one correspondence with twisted Ward left quasigroups, which are left quasigroups satisfying the identity $(x*y)*(x*z)=(y*y)*(y*z)$. Using combinatorial properties of t
Externí odkaz:
http://arxiv.org/abs/2002.02854
Autor:
Drápal, Aleš, Vojtěchovský, Petr
We introduce the concept of propagating equations and focus on the case of associativity propagating in varieties of loops. An equation $\varepsilon$ propagates in an algebra $X$ if $\varepsilon(\overrightarrow y)$ holds whenever $\varepsilon(\overri
Externí odkaz:
http://arxiv.org/abs/2001.09167