Connections between loops of exponent 2, reflection structures and complete graphs with parallelism (Q1578473)

In the present paper the author considers the particular situation where \((L,+)\) is a loop of exponent 2 and it will be related to both a reflection structure and to a complete graph with parallelism \((L,{L\choose 2},|\;|)\). The connections between these structures, under further conditions as well, are studied in this paper via Theorems 1 and 2.