2020/07/16 by Mark Greer, Greer, Mark, Lee Raney +1
Engineering · Mathematics · #20N05 #FOS: Mathematics #Group Theory (math.GR) #History and Theory of Mathematics #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2007.08419
openalex publication_date 2020/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a uniquely 2-divisible group G, we study a commutative loop (G,∘) which arises as a result of a construction in \citebaer. We investigate some general properties and applications of ∘ and determine a necessary and sufficient condition on G in order for (G, ∘) to be Moufang. In \citegreer14, it is conjectured that G is metabelian if and only if (G, ∘) is an automorphic loop. We answer a portion of this conjecture in the affirmative: in particular, we show that if G is a split metabelian group of odd order, then (G, ∘) is automorphic.