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pro vyhledávání: '"Drápal, Aleš"'
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:
Drápal, Aleš, Wanless, Ian M.
Publikováno v:
Proc. Edinburgh Math. Soc. 66 (2023), 1085-1109
Let $\mathbb{F}$ be a finite field of odd order and $a,b\in\mathbb{F}\setminus\{0,1\}$ be such that $\chi(a) = \chi(b)$ and $\chi(1-a)=\chi(1-b)$, where $\chi$ is the extended quadratic character. Let $Q_{a,b}$ be the quasigroup upon $\mathbb{F}$ def
Externí odkaz:
http://arxiv.org/abs/2211.09472
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:
Drápal, Aleš, Kinyon, Michael
Publikováno v:
Commentationes Mathematicae Universitatis Carolinae 61 (2020), no. 4, 481-500
Let $Q$ be a loop. If $S\leq Q$ is such that $\varphi(S) \subseteq S$ for each standard generator of $\mathrm{Inn}(Q)$, then $S$ does not have to be a normal subloop. In an LC loop the left and middle nucleus coincide and form a normal subloop. The i
Externí odkaz:
http://arxiv.org/abs/2006.08734