Minimal monoids generating varieties with complex subvariety lattices
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914803445923840 |
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| author | Gusev, Sergey V. |
| author_facet | Gusev, Sergey V. |
| contents | A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely universal variety of monoids and, by the previous results, it is the smallest generator for a monoid variety with this property. It is also deduced that the join of two Cross varieties of monoids can be finitely universal. In particular, we exhibit a finitely universal variety of monoids with uncountably many subvarieties which is the join of two Cross varieties of monoids whose lattices of subvarieties are the 6-element and the 7-element chains, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16012 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Minimal monoids generating varieties with complex subvariety lattices Gusev, Sergey V. Group Theory 20M07, 08B15 A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely universal variety of monoids and, by the previous results, it is the smallest generator for a monoid variety with this property. It is also deduced that the join of two Cross varieties of monoids can be finitely universal. In particular, we exhibit a finitely universal variety of monoids with uncountably many subvarieties which is the join of two Cross varieties of monoids whose lattices of subvarieties are the 6-element and the 7-element chains, respectively. |
| title | Minimal monoids generating varieties with complex subvariety lattices |
| topic | Group Theory 20M07, 08B15 |
| url | https://arxiv.org/abs/2211.16012 |