Equationally complete varieties of generalized groups

Abstract

In previous work, Page and Butson [Algebra Universalis 3 (1973), 112-126] characterized all equationally complete classes (atoms) of m-semigroups (universal algebras with one m-ary associative operation), and hence /n-groups, in the commutative case. The further characterization of the non-commutative m-group atoms was thought to hinge upon a conjecture by Page [PhD thesis,-University of Miami, 1973] that a weaker form of commutativity held true. In this paper that conjecture is proved and then used to study the special case m = k . Two additional infinite sets of atoms are thereby determined, although i t is not proved that these examples exhaust the remaining atoms for m = h .