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104573 Commentationes Mathematicae Universitatis Carolinae Comment. Math. Univ. Carolin. 0010-2628 1213-7243 Charles University in Prague, Faculty of Mathematics and Physics Praha Czech Republic

Commentationes Mathematicae Universitatis Carolinae (founded by E. Čech) is a quarterly periodical published by the Faculty of Mathematics and Physics of Charles University, Prague, Czech Republic. It contains important research articles and a limited number of invited survey articles, covering pure as well as applied mathematics.

 142931 math Pseudoautomorphisms of Bruck loops and their generalizations Greer Mark Kinyon Michael 2012 53 141821 3 142927 3 383 389 3017837 1256.20062 MetaFull (TXT) MetaFull (PDF) Access to full text Full (PDF)

We show that in a weak commutative inverse property loop, such as a Bruck loop, if $\alpha$ 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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