Isomorphism Theorems for Groupoids and Some Applications
Using an algebraic point of view we present an introduction to the groupoid theory; that is, we give fundamental properties of groupoids as uniqueness of inverses and properties of the identities and study subgroupoids, wide subgroupoids, and normal subgroupoids. We also present the isomorphism theo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/3967368 |
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| _version_ | 1849690597090131968 |
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| author | Jesús Ávila Víctor Marín Héctor Pinedo |
| author_facet | Jesús Ávila Víctor Marín Héctor Pinedo |
| author_sort | Jesús Ávila |
| collection | DOAJ |
| description | Using an algebraic point of view we present an introduction to the groupoid theory; that is, we give fundamental properties of groupoids as uniqueness of inverses and properties of the identities and study subgroupoids, wide subgroupoids, and normal subgroupoids. We also present the isomorphism theorems for groupoids and their applications and obtain the corresponding version of the Zassenhaus Lemma and the Jordan-Hölder theorem for groupoids. Finally, inspired by the Ehresmann-Schein-Nambooripad theorem we improve a result of R. Exel concerning a one-to-one correspondence between partial actions of groups and actions of inverse semigroups. |
| format | Article |
| id | doaj-art-eb55cace4d214fe09e519453356f382e |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-eb55cace4d214fe09e519453356f382e2025-08-20T03:21:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/39673683967368Isomorphism Theorems for Groupoids and Some ApplicationsJesús Ávila0Víctor Marín1Héctor Pinedo2Departamento de Matemáticas y Estadística, Universidad del Tolima, Santa Helena, Ibagué, ColombiaDepartamento de Matemáticas y Estadística, Universidad del Tolima, Santa Helena, Ibagué, ColombiaEscuela de Matemáticas, Universidad Industrial de Santander, Cra. 27 calle 9, Bucaramanga, ColombiaUsing an algebraic point of view we present an introduction to the groupoid theory; that is, we give fundamental properties of groupoids as uniqueness of inverses and properties of the identities and study subgroupoids, wide subgroupoids, and normal subgroupoids. We also present the isomorphism theorems for groupoids and their applications and obtain the corresponding version of the Zassenhaus Lemma and the Jordan-Hölder theorem for groupoids. Finally, inspired by the Ehresmann-Schein-Nambooripad theorem we improve a result of R. Exel concerning a one-to-one correspondence between partial actions of groups and actions of inverse semigroups.http://dx.doi.org/10.1155/2020/3967368 |
| spellingShingle | Jesús Ávila Víctor Marín Héctor Pinedo Isomorphism Theorems for Groupoids and Some Applications International Journal of Mathematics and Mathematical Sciences |
| title | Isomorphism Theorems for Groupoids and Some Applications |
| title_full | Isomorphism Theorems for Groupoids and Some Applications |
| title_fullStr | Isomorphism Theorems for Groupoids and Some Applications |
| title_full_unstemmed | Isomorphism Theorems for Groupoids and Some Applications |
| title_short | Isomorphism Theorems for Groupoids and Some Applications |
| title_sort | isomorphism theorems for groupoids and some applications |
| url | http://dx.doi.org/10.1155/2020/3967368 |
| work_keys_str_mv | AT jesusavila isomorphismtheoremsforgroupoidsandsomeapplications AT victormarin isomorphismtheoremsforgroupoidsandsomeapplications AT hectorpinedo isomorphismtheoremsforgroupoidsandsomeapplications |