Abstract:In this paper we consider finite loops whose inner mapping groups are nilpotent. We first consider the case where the inner mapping group $I(Q)$ of a loop $Q$ is the direct product of a dihedral group of order $8$ and an abelian group. Our second result deals with the case where $Q$ is a $2$-loop and $I(Q)$ is a nilpotent group whose nonabelian Sylow subgroups satisfy a special condition. In both cases it turns out that $Q$ is centrally nilpotent.
Keywords: loop, group, connected transversals
AMS Subject Classification: 20D10, 20N05