Maximal Subsemigroups of Infinite Symmetric Inverse Monoids
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908530269749248 |
|---|---|
| author | Hampenberg, M. Péresse, Y. |
| author_facet | Hampenberg, M. Péresse, Y. |
| contents | The symmetric inverse monoid $I_X$ on a set $X$ consists of all bijective functions whose domain and range are subsets of $X$ under the usual composition and inversion of partial functions. For an arbitrary infinite set $X$, we classify all maximal subsemigroups and maximal inverse subsemigroups of $I_X$ which contain the symmetric group Sym($X$) or any of the following subgroups of Sym($X$): the pointwise stabiliser of a finite subset of $X$, the stabiliser of an ultrafilter on $X$, or the stabiliser of a partition of $X$ into finitely many parts of equal cardinality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal Subsemigroups of Infinite Symmetric Inverse Monoids Hampenberg, M. Péresse, Y. Rings and Algebras Group Theory 20M20 (Primary) 20M18, 20E28, 03E75 (Secondary) The symmetric inverse monoid $I_X$ on a set $X$ consists of all bijective functions whose domain and range are subsets of $X$ under the usual composition and inversion of partial functions. For an arbitrary infinite set $X$, we classify all maximal subsemigroups and maximal inverse subsemigroups of $I_X$ which contain the symmetric group Sym($X$) or any of the following subgroups of Sym($X$): the pointwise stabiliser of a finite subset of $X$, the stabiliser of an ultrafilter on $X$, or the stabiliser of a partition of $X$ into finitely many parts of equal cardinality. |
| title | Maximal Subsemigroups of Infinite Symmetric Inverse Monoids |
| topic | Rings and Algebras Group Theory 20M20 (Primary) 20M18, 20E28, 03E75 (Secondary) |
| url | https://arxiv.org/abs/2509.08468 |