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pro vyhledávání: '"Marco Bonatto"'
Publikováno v:
Journal of Algebra. 567:284-309
We introduce the notion of an orbit series in a quandle. Using this notion we define four families of quandles based on finiteness conditions on their orbit series. Intuitively, the classes tOS and tOSn correspond to finitary compositions of trivial
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https://doi.org/10.1016/j.jalgebra.2020.09.026
https://doi.org/10.1016/j.jalgebra.2020.09.026
Autor:
Emiliano Acri, Marco Bonatto
Publikováno v:
Communications in Algebra. 48:1872-1881
We construct all skew braces of size $pq$ (where $p>q$ are primes) by using Byott's classification of Hopf--Galois extensions of the same degree. For $p\not\equiv 1 \pmod{q}$ there exists only one skew brace which is the trivial one. When $p\equiv 1
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https://doi.org/10.1080/00927872.2019.1709480
https://doi.org/10.1080/00927872.2019.1709480
Autor:
Marco Bonatto
Publikováno v:
Monatshefte für Mathematik. 191:691-717
In the paper we describe the class of principal quandles and we show that connected quandles can be decomposed as a disjoint union of principal quandles. We also prove that simple affine quandles are finite and they can be characterized among finite
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https://doi.org/10.1007/s00605-019-01334-1
https://doi.org/10.1007/s00605-019-01334-1
Autor:
Marco Bonatto, E. Acri
Publikováno v:
Journal of Algebra and Its Applications. 21
In this paper we enumerate the skew braces of non-abelian type of size $p^2q$ for $p,q$ primes with $q>2$ by the classification of regular subgroups of the holomorph of the non-abelian groups of the same order. Since Crespo dealt with the case $q=2$,
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https://doi.org/10.1142/s0219498822500621
https://doi.org/10.1142/s0219498822500621
Autor:
Marco Bonatto
In this paper, we investigate the class of semimedial left quasigroups, a class that properly contains racks and medial left quasigroups. We extend most of the results about commutator theory for racks collected in [M. Bonatto and D. Stanovský, Comm
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http://arxiv.org/abs/2004.05370
http://arxiv.org/abs/2004.05370
Autor:
Marco Bonatto, Giuliano Bianco
We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size $$p^3$$ for $$p>3$$ , using a combination of group theoretical and universal algebraic tools. As a byproduct we obtain
Externí odkaz:
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http://arxiv.org/abs/1904.12801
http://arxiv.org/abs/1904.12801
Wolfgang Rump showed that there is a one-to-one correspondence between nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation and binary algebras in which all left translations L x are bijections, the squaring map is a bijection
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c9e44d1cff3a7ed817b2466509fda5b5
Autor:
Marco Bonatto, David Stanovský
Publikováno v:
J. Math. Soc. Japan 73, no. 1 (2021), 41-75
We adapt the commutator theory of universal algebra to the particular setting of racks and quandles, exploiting a Galois connection between congruences and certain normal subgroups of the displacement group. Congruence properties, such as abelianness
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We continue the study of the quandle of homomorphisms into a medial quandle begun in Crans and Nelson. We show that it suffices to consider only medial source quandles, and therefore the structure theorem of Jedlicka et al. provides a characterizatio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a02158ca1b14247f8bdf9d6f572224c1
Autor:
Marco Bonatto, Petr Vojtěchovský
A (left) quandle is connected if its left translations generate a group that acts transitively on the underlying set. In 2014, Eisermann introduced the concept of quandle coverings, corresponding to constant quandle cocycles of Andruskiewitsch and Gr
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