Non-dyadic Laver algebras

We study finite Laver algebras, the generalizations of Laver tables on sets of cardinality not of the form $2^n$. We characterize the conditions under which projections and embeddings between Laver algebras exist and show that there are $2^{{\mathrm{\aleph }}_0}$ pairwise non-isomorphic direct limits of finite Laver algebras.