On the uniqueness of loops M(G,2)

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 $i$, $j\in C_2$. When $G$ is nonabelian then exactly four assignments yield Moufang loops that are not associative; all (anti)isomorphic, known as loops $M(G,2)$.

5 pages, revised, the published version contains an error, see "A class of Bol loops with a subgroup of index two" by P.V. for more details

Cited by in corpus (2)

• Loops of Bol-Moufang type with a subgroup of index two
• A class of Bol loops with a subgroup of index two