Publication
Minimal paths in the commuting graphs of semigroups
| dc.contributor.author | Araújo, João | |
| dc.contributor.author | Kinyon, Michael | |
| dc.contributor.author | Konieczny, Janusz | |
| dc.date.accessioned | 2011-12-19T15:17:14Z | |
| dc.date.available | 2011-12-19T15:17:14Z | |
| dc.date.issued | 2011 | |
| dc.description.abstract | Let S be a finite non-commutative semigroup. The commuting graph of S, denoted G(S), is the graph whose vertices are the non- central elements of S and whose edges are the sets {a, b} of vertices such that a �= b and ab = ba. Denote by T(X) the semigroup of full transformations on a finite set X . Let J be any ideal of T (X ) such that J is different from the ideal of constant transformations on X. We prove that if |X| ≥ 4, then, with a few exceptions, the diameter of G(J ) is 5. On the other hand, we prove that for every positive integer n, there exists a semigroup S such that the diameter of G(S) is n. We also study the left paths in G(S), that is, paths a1 − a2 − ··· − am such that a1 �= am and a1ai = amai for all i ∈ {1,...,m}. We prove that for every positive integer n ≥ 2, except n = 3, there exists a semigroup whose shortest left path has length n. As a corollary, we use the previous results to solve a purely algebraic old problem posed by B.M. Schein. | por |
| dc.identifier.citation | Araújo, João; Kinyon, Michael; Konieczny, Janusz - "European Journal of Combinatorics" [Em linha]. ISSN 0195-6698. Vol. 32, nº 2 (2011), p. 178-197 | por |
| dc.identifier.uri | http://hdl.handle.net/10400.2/2007 | |
| dc.language.iso | eng | por |
| dc.peerreviewed | yes | por |
| dc.publisher | Elsevier | por |
| dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0195669810001265 | por |
| dc.subject | Groups | |
| dc.title | Minimal paths in the commuting graphs of semigroups | por |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 197 | por |
| oaire.citation.startPage | 178 | por |
| oaire.citation.title | European Journal of Combinatorics | por |
| person.familyName | Ribeiro Soares Gonçalves de Araújo | |
| person.familyName | Kinyon | |
| person.givenName | João Jorge | |
| person.givenName | Michael Kinyon | |
| person.identifier.ciencia-id | EC1F-273A-9F24 | |
| person.identifier.ciencia-id | 2A10-E0DD-5A23 | |
| person.identifier.orcid | 0000-0001-6655-2172 | |
| person.identifier.orcid | 0000-0002-5227-8632 | |
| rcaap.rights | restrictedAccess | por |
| rcaap.type | article | por |
| relation.isAuthorOfPublication | 1f7b349c-3251-480d-a3ac-e3cb4ef44f22 | |
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