An automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. An open problem was: Does every finite automorphic loop have the elementwise Lagrange property? We give a positive answer to this problem.
"All finite automorphic loops have the elementwise Lagrange property." Rocky Mountain J. Math. 45 (4) 1101 - 1105, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1101