强极小Steiner系统II:配位与拟群

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2023-05-02 DOI:10.1007/s00012-023-00812-w

John T. Baldwin

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引用次数: 1

摘要

如果k是素数幂，则每个强极小Steiner k-系统（M，R）（其中R是三元共线关系）可以在（Ganter–Werner 1975）意义上由拟群“配位”。我们证明了这种配位在（M，R）中是不可定义的，并且在（Baldwin–Paolini 2020）中构造的强极小Steiner k-系统从未解释拟群。然而，通过改进构造，如果k是素数幂，则在每个（2，k）-类拟群（定义3.10）中，都存在一个强极小拟群，它解释Steiner k系统。

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Strongly minimal Steiner systems II: coordinatization and quasigroups

Each strongly minimal Steiner k-system (M, R) (where is R is a ternary collinearity relation) can be ‘coordinatized’ in the sense of (Ganter–Werner 1975) by a quasigroup if k is a prime-power. We show this coordinatization is never definable in (M, R) and the strongly minimal Steiner k-systems constructed in (Baldwin–Paolini 2020) never interpret a quasigroup. Nevertheless, by refining the construction, if k is a prime power, in each (2, k)-variety of quasigroups (Definition 3.10) there is a strongly minimal quasigroup that interprets a Steiner k-system.

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来源期刊

Algebra Universalis 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3 months

期刊介绍： Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.