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http://hdl.handle.net/20.500.12188/1965| Title: | Cyclic subgroupoids of an absolutely free groupoid | Authors: | Celakoska-Jordanova, Vesna | Keywords: | groupoid, subgroupoid, generating element, cyclic subgroupoid, free groupoid. | Issue Date: | 2007 | Publisher: | Union of Mathematicians of Macedonia | Journal: | Proceedings of III Congress of Mathematicians of Macedonia, Struga, R. Macedonia, 29.IX.2005-2.X.2005 | Conference: | III Congress of Mathematicians of Macedonia, Struga, R. Macedonia, 29.IX.2005-2.X.2005 | Abstract: | Subgroupoids of an absolutely free groupoid F = (F,⋅) with a free basis B that are generated by one element (called cyclic subgroupoids of F ) are considered. It is shown that: two cyclic subgroupoids of F have common elements if and only if one of them is contained in the other; F has maximal cyclic subgroupoids and if card(B) ≥ 2 , every cyclic subgroupoid is contained in a maximal one; any two maximal cyclic subgroupoids of F are either disjoint or equal. Also, a characterization of maximal cyclic subgroupoids of F by means of primitive elements in F is given. This statements are also true for an absolutely free groupoid with one-element basis (with modified definition of maximal cyclic subgroupoid). | URI: | http://hdl.handle.net/20.500.12188/1965 |
| Appears in Collections: | Faculty of Natural Sciences and Mathematics: Conference papers |
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| Cyclic subgroupoids of an absolutely free groupoid.pdf | 227.81 kB | Adobe PDF |  View/Open |
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