Regular subgroups of the affine group and asymmetric product of radical braces

Catino, Francesco; Colazzo, Ilaria; Stefanelli, Paola

doi:10.1016/j.jalgebra.2016.01.038

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Introduction3

Indecomposable Cycle Sets Of Cardinality Pq and Cyclic Permu1

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Cited by 42 publications

(48 citation statements)

References 9 publications

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“…for every k ∈ Z/pZ, where kt is the representative of kt in {0, ..., p − 1}. Conversely, every maps of type (7) satisfies (6). In particular there are (p − 1) bijections of this type.…”

Section: Indecomposable Cycle Sets Of Cardinality Pq and Cyclic Permumentioning

confidence: 99%

On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size

Castelli

Pinto

Rump

2020

Communications in Algebra

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Section: Indecomposable Cycle Sets Of Cardinality Pq and Cyclic Permumentioning

confidence: 99%

On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size

Castelli

Pinto

Rump

2020

Communications in Algebra

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“…13 implies that the sum of all Baer radical ideals in A is the largest Baer radical ideal in A. Thus a skew brace A contains largest Baer radical ideal.…”

mentioning

confidence: 97%

On skew braces and their ideals

Konovalov

Smoktunowicz

Vendramin

2018

Experimental Mathematics

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“…As reformulated by Cedó, Jespers, and Okńinski in [13], a left brace is a set B with two operations + and • such that (B, +) is an abelian group, (B, •) is a group and the relation a • (b + c) + a = a • b + a • c holds for all a, b, c ∈ B. Braces have been widely studied, see for instance [30,8,19,31,3,1,11,25]. Soloviev in [33] and Lu, Yan, and Zhu in [26] studied bijective not necessarily involutive solutions.…”

Section: Introductionmentioning

confidence: 99%

The Matched Product of the Solutions to the Yang–Baxter Equation of Finite Order

2020

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In this work, we focus on the set-theoretical solutions of the Yang-Baxter equation which are of finite order and not necessarily bijective. We use the matched product of solutions as a unifying tool for treating these solutions of finite order, that also include involutive and idempotent solutions. In particular, we prove that the matched product of two solutions rS and rT is of finite order if and only if rS and rT are. Furthermore, we show that with sufficient information on rS and rT we can precisely establish the order of the matched product. Finally, we prove that if B is a finite semi-brace, then the associated solution r satisfies r n = r, for an integer n closely linked with B.Mathematics Subject Classification (2010). Primary 16T25; Secondary 81R50, 16Y99, 16N20.

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Regular subgroups of the affine group and asymmetric product of radical braces

Cited by 42 publications

References 9 publications

On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size

On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size

On skew braces and their ideals

The Matched Product of the Solutions to the Yang–Baxter Equation of Finite Order

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