A nuclear construction of loops with small inner mapping groups

摘要

We construct an infinite class of left conjugacy closed loopsQ such that the inner mapping group InnQ is a nonabelian group of orderpq. The constructions are done in a broader context of loopsQ =N _λ N _ρ such thatN _λ =N _μ ⊴Q and InnQ can be embedded into the holomorph of a cyclic group.