On Products of Finite Nilpotent Groups.
Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.
We consider a smooth projective variety on which a simple algebraic group acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of with the induced action of on the normal bundle of a closed orbit of the action. We get effective results in case and .