Enumeration of AG-groupoids

Authors:
Andreas Distler;Muhammad Shah;Volker Sorge
Affiliations:
Universidade de Lisboa, Lisboa, Portugal;Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan;School of Computer Science, The University of Birmingham, Birmingham, UK
Venue:
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Year:
2011

Citing 4
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Abstract

Enumeration and classification of mathematical entities is an important part of mathematical research in particular in finite algebra. For algebraic structures that are more general than groups this task is often only feasible by use of computers due to the sheer number of structures that have to be considered. In this paper we present the enumeration and partial classification of AG-groupoids -- groupoids in which the identity (ab)c = (cb)a holds -- of up to order 6. The results are obtained with the help of the computer algebra system GAP and the constraint solver Minion by making use of both algebraic techniques as well as search pruning via symmetry breaking.