A class of Bol loops with a subgroup of index two

Abstract

Let $G$ be a finite group and $C_2$ the cyclic group of order 2. Consider the 8 multiplicative operations $(x,y)\mapsto (x^i{y}^j{)}^k$, 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. Vojtěchovský: On the uniqueness of loops $M(G,2)$.

10 pages

References in corpus (1)

• On the uniqueness of loops M(G,2)