Pseudoautomorphisms of Bruck loops and their generalizations
We show that in a weak commutative inverse property loop, such as a Bruck loop, if α is a right [left] pseudoautomorphism with companion c, then c [c2] must lie in the left nucleus. In particular, for any such loop with trivial left nucleus, every right pseudoautomorphism is an automorphism and if the squaring map is a permutation, then every left pseudoautomorphism is an automorphism as well. We also show that every pseudoautomorphism of a commutative inverse property loop is an automorphism, generalizing a well-known result of Bruck.
Commentationes Mathematicae Universitatis Carolinae
Greer, M., & Kinyon, M. (2012). Pseudoautomorphisms of Bruck loops and their generalizations. Commentationes Mathematicae Universitatis Carolinae. Retrieved from https://ir.una.edu/math_facpub/8