Varieties generated by two element non-associative groupoids (Q2710259)

There are 16 different binary groupoids on the set of two elements \(\{a,b\}\), 8 of them are associative and 8 of them are non-associative. Moreover, among non-associative groupoids three pairs are isomorphic, thus there remain 5 non-isomorphic, non-associative groupoids, which are investigated in this paper. The main result is the answer to the question: which of the varieties generated by two element non-associative groupoids are atoms (minimal)?NEWLINENEWLINEFor the entire collection see [Zbl 0940.00021].