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Divisor graphs and isotopy invariants of commutative quasigroups
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2021-12-13 , DOI: 10.1016/j.jcta.2021.105577
John D. LaGrange

Given an element x of a commutative quasigroup A, the x-divisor graph of A is the graph Γx(A) whose vertices are the elements of A such that distinct vertices a and b are adjacent if and only if ab=x. This paper examines how isotopies act on the set {Γx(A) | xA}. It is shown that if |A|< is not a multiple of 4, then this set is an isotopy invariant. Moreover, under certain conditions (for example, when A is isotopic to a group), the commutative quasigroup isotopes of A are completely determined by symmetries of {Γx(A) | xA}.



中文翻译:

可交换拟群的除数图和同位素不变量

给定可交换拟群的元素x一个, x -除数图一个 是图 ΓX(一个) 其顶点是 一个使得不同的顶点ab相邻当且仅当一个=X. 本文研究了同位素如何作用于集合{ΓX(一个) | X一个}. 结果表明,如果|一个|<不是 4 的倍数,则该集合是同位素不变量。此外,在某些条件下(例如,当一个 是一个群的同位素), 的交换准群同位素 一个 完全由对称性决定 {ΓX(一个) | X一个}.

更新日期:2021-12-14
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