  We describe generators of universal Lefschetz groups consisting of self-maps
of equivariant 1-spheres. This allows to formulate a normalization axiom which,
together with the usual axioms, determines an equivariant Lefschetz number
uniquely. We apply this technique to identify the fixed orbit detecting
equivariant Lefschetz number of Chorny with the fixed orbit index of Dzedzej.
