  Groups are usually axiomatized as algebras with an associative binary
operation, a two-sided neutral element, and with two-sided inverses. We show in
this note that the same simplicity of axioms can be achieved for some of the
most important varieties of loops. In particular, we investigate loops of
Bol-Moufang type in the underlying variety of magmas with two-sided inverses,
and obtain "group-like" equational bases for Moufang, Bol and C-loops. We also
discuss the case when the inverses are only one-sided and/or the neutral
element is only one-sided.
