The article examines Bol loops that are constructed from matched pairs of groups, including a new simple, non-Moufang Bol loop of order 120. Certain permutation representations of the loops under consideration provide nontrivial examples of doubly stochastic action matrices. A generalization of the matched-pair loop construction yields proper Bol actions of groups.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory