Abstract
Let A be a finite set, n -> 1 and D C A ". We say that f : D ~ A is a functionally complete partial operation of size I D ( if each f* : A" ~ A agreeing with ( on D is functionally complete. Such an operation of size d represents thus a family of IA I (IAIL~) functionally complete operations. We investigate the least possible size of functionally complete partial groupoids. Such groupoids not defined on a row or column have size either I A L+ 1 or I A I + 2 or are of size at least 2 ) A I - 2. We prove that ( A ( + 1 is the least size of such a groupoid and completely determine those of size I A ( + 1. As one might expect, these groupoids are very special. This study shows how surprisingly little information is needed to ensure that a groupoid is functionally complete and, at the same time, gives a description of large classes of functionally complete groupoids.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
