On loop identities that can be obtained by a nuclear identification

We start by describing all the varieties of loops Q that can be defined by autotopisms α x , x ∈ Q , where α x is a composition of two triples, each of which becomes an autotopism when the element x belongs to one of the nuclei. In this way we obtain a unifying approach to Bol, Moufang, extra, Buchsteiner and conjugacy closed loops. We re-prove some classical facts in a new way and show how Buchsteiner loops fit into the traditional context. We also describe a new class of loops with coinciding left and right nuclei. These loops have remarkable properties and do not belong to any of the classical classes.