From involution sets, graphs and loops to loop-nearrings

This is a general frame for a theory which connects the areas of loops, involution sets and graphs with parallelism. Our main results are stated in 5, 6 and 7. In 5 we derive a partial binary operation from an involution set and we discuss if such operation is a, Bol operation or a K-operation, in 6, we relate involution sets with loops. In 7 we look for the possibility to construct loop-nearrings by considering the automorphism groups of loops.