Subject: groupoid, subgroupoid, generating element, cyclic subgroupoid, free groupoid.
Year: 2007
Type: Article
Title: Cyclic subgroupoids of an absolutely free groupoid
Author: Celakoska-Jordanova, Vesna
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).
Publisher: Union of Mathematicians of Macedonia
Relation: Proceedings of III Congress of Mathematicians of Macedonia, Struga, R. Macedonia, 29.IX.2005-2.X.2005
Identifier: oai:repository.ukim.mk:20.500.12188/1965
Identifier: http://hdl.handle.net/20.500.12188/1965
