2012/04/26 by Mark Greer, Michael Kinyon, Greer, Mark +1
Mathematics · #20N05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20N05
paper · pdf · doi:10.48550/arxiv.1204.6075
to appear in Comment. Math. Univ. Carolin
arxiv created 2012/04/26 · arxiv updated 2012/04/30
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.