Effects of semigroup properties on local embeddability
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908609926922240 |
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| author | Kudryavtsev, Dmitry |
| author_facet | Kudryavtsev, Dmitry |
| contents | We investigate whether semigroups with a given property which are also locally embeddable into finite semigroups can be locally embedded into finite semigroups with the same property, obtaining a positive answer for completely simple and Clifford semigroups (similarly to group and inverse semigroup cases studied previously) and a negative answer for $\J$-trivial semigroups (similarly to cancellative semigroups). Additionally, we resolve the standing question on the differences between local embeddability in and local wrappability by finite structures, providing a novel construction of $\J$-trivial semigroups which satisfy the latter, but not the former. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effects of semigroup properties on local embeddability Kudryavtsev, Dmitry Group Theory 20M10, 20M15, 20M18 We investigate whether semigroups with a given property which are also locally embeddable into finite semigroups can be locally embedded into finite semigroups with the same property, obtaining a positive answer for completely simple and Clifford semigroups (similarly to group and inverse semigroup cases studied previously) and a negative answer for $\J$-trivial semigroups (similarly to cancellative semigroups). Additionally, we resolve the standing question on the differences between local embeddability in and local wrappability by finite structures, providing a novel construction of $\J$-trivial semigroups which satisfy the latter, but not the former. |
| title | Effects of semigroup properties on local embeddability |
| topic | Group Theory 20M10, 20M15, 20M18 |
| url | https://arxiv.org/abs/2510.21349 |