The study of paramedial groupoids (with emphasis on the structure of simple paramedial groupoids) was initiated in [1] and continued in [2], [3] and [5]. The aim of the present paper is to give a full description of finite simple zeropotent paramedial groupoids (i.e., of finite simple paramedial groupoids of type (II)—see [2]). A reader is referred to [1], [2], [3] and [7] for notation and various prerequisites.
The paper is an immediate continuation of [3], where one can find various notation and other useful details. In the present part, a full classification of infinite simple zeropotent paramedial groupoids is given.
By a paramedial groupoid we mean a groupoid satisfying the equation ax·yb=bx·ya. This equation is, in certain sense, symmetric to the equation of mediality xa·by=xb·ay and, in fact, the theories of both varieties of groupoids are parallel. The present paper, initiating the study of paramedial groupoids, is meant as a modest contribution to the enormously difficult task of describing algebraic properties of varieties determined by strong linear identities (and, especially,of the corresponding simple algebras).