Abstract:Let $G$ be a finite group and $C_2$ the cyclic group of order $2$. Consider the $8$ multiplicative operations $(x,y)\mapsto (x^iy^j)^k$, where $i$, $j$, $k\in \{-1, 1\}$. Define a new multiplication on $G\times C_2$ by assigning one of the above $8$ multiplications to each quarter $(G\times \{i\})\times (G\times \{j\})$, for $i, j\in C_2$. We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P. Vojt\v {e}chovsk\'y: On the uniqueness of loops $M(G,2)$.
Keywords: Moufang loops, loops $M(G,2)$, inverse property loops, Bol loops
AMS Subject Classification: 20N05