2022/03/11 by Maria de Lourdes Merlini Giuliani, Giuliani, Maria de Lourdes Merlini, Giliard Souza dos Anjos +1
Engineering · Mathematics · #20N05 #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2203.06230
openalex publication_date 2022/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Automorphic loops are loops in which all inner mappings are automorphisms. This variety of loops includes groups and commutative Moufang loops. A half-isomorphism f : G \longrightarrow K between multiplicative systems G and K is a bijection from G onto K such that f(ab)∈\f(a)f(b), f(b)f(a)\ for any a,b∈ G. A half-isomorphism is trivial when it is either an isomorphism or an anti-isomorphism. Consider the class of automorphic loops such that the equation x⋅(x⋅ y) = (y⋅ x)⋅ x is equivalent to x⋅ y = y⋅ x. Here we show that this class of loops includes automorphic loops of odd order and uniquely 2-divisible. Furthermore, we prove that every half-isomorphism between loops in that class is trivial.