Small monoids generating varieties with uncountably many subvarieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909481874489344 |
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| author | Gusev, Sergey V. |
| author_facet | Gusev, Sergey V. |
| contents | An algebra that generates a variety with uncountably many subvarieties is said to be of type $2^{\aleph_0}$. We show that the Rees quotient monoid $M(aabb)$ of order ten is of type $2^{\aleph_0}$, thereby affirmatively answering a recent question of Glasson. As a corollary, we exhibit a new example of type $2^{\aleph_0}$ monoid of order six, which turns out to be minimal and the first of its kind that is finitely based. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_15554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small monoids generating varieties with uncountably many subvarieties Gusev, Sergey V. Group Theory 20M07 An algebra that generates a variety with uncountably many subvarieties is said to be of type $2^{\aleph_0}$. We show that the Rees quotient monoid $M(aabb)$ of order ten is of type $2^{\aleph_0}$, thereby affirmatively answering a recent question of Glasson. As a corollary, we exhibit a new example of type $2^{\aleph_0}$ monoid of order six, which turns out to be minimal and the first of its kind that is finitely based. |
| title | Small monoids generating varieties with uncountably many subvarieties |
| topic | Group Theory 20M07 |
| url | https://arxiv.org/abs/2411.15554 |