Characteristic subgroup of a covering

Let be a covering. The characteristic subgroup¹ is a subgroup of the fundamental group of given by #m/def/homotopy

Properties

A covering is injective on the fundamental group
The Sheet number of a connected covering is the index of the characteristic subgroup within the entire fundamental group
Two coverings are equivalent iff their characteristic subgroups match
Basepoint independent: Characteristic conjugacy class of a path-connected covering

#state/tidy | #lang/en | #SemBr

This term does not appear to be remotely established in the literature. My guess is it is a coinage by Frank Loose. ↩