Transversals in loops. 3. Loop transversals

The investigation of the new notion of a transversal in a loop to its subloop (begun in [10]) is continued in the present article. This notion generalized the well-known notion of a transversal in a group to its subgroup and can be correctly defined only in the case when some specific condition (Condition A) for a loop and its subloop holds. The connections between loop transversals in some loop to its subloop and loop transversals in multiplicative group of this loop to some suitable subgroup are investigated in this work.