Kikkawa left loops and Symmetric 2-structures

We approach the existence of class 1 symmetric 2-structures by studying a class of left loops related to them. Such left loops turn out to satisfy a relation very similar to the left Bol property, and they are of exponent 2. Then we give a characterization of these left loops by means of invariant involution sets, and classify them according to the cardinality of the point stabilizers, comparing then our results with the classification of symmetric 2-structures given in [3].