Title

Pseudoautomorphisms of Bruck loops and their generalizations

Document Type

Article

Publication Date

12-1-2012

Abstract

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.

Publication Title

Commentationes Mathematicae Universitatis Carolinae

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