On loops rich in automorphisms that are abelian modulo the nucleus

Abstract

We prove that a loop has to be conjugacy closed modulo modulo the center whenever all standard left inner mappings and all standard right inner mappings are automorphisms, the nucleus is a normal subloop, the factor over nucleus is an abelian group, and the left multiplication group is a normal subgroup of the multiplication group.

Keywords

• loops
• automorphisms
• abelian
• modulo
• nucleus