Pseudoautomorphisms of Bruck loops and their generalizations

Mark Greer; Michael Kinyon

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arXiv · 1204.6075

Pseudoautomorphisms of Bruck loops and their generalizations

Mark Greer·Michael Kinyon

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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 $c$ [$c^2$] 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.

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BibTeX RIS

Mark Greer, Michael Kinyon. 2012-04-26. Pseudoautomorphisms of Bruck loops and their generalizations. https://arxiv.org/abs/1204.6075

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