Matched Pairs, Permutation Representations, and the Bol Property

Abstract

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.

Key Words:

• Bol loop
• Doubly stochastic
• Dual code
• Group action
• Group factorization
• Matched pair
• Permutation representation

2000 Mathematics Subject Classification:

• 20N05
• 20D40
• 20B99

ACKNOWLEDGMENTS

We are grateful to M. Kinyon and an anonymous referee for helpful observations on the content of this article.

Notes

Communicated by I. Shestakov.