- #1

- 713

- 5

in group theory a

*regular*action on a

*G*-set

*S*is such that for every x,y∈

*S*, there exists exactly one

*g*such that g⋅x = y.

I noticed however that in the theory of Lie groups the definition of regular action is quite different (see Definition 1.4.8 at this link).

Is there a connection between the two definition? I would like to understand why a regular Lie group action is defined in that way.

Thanks.