(I'm not a mathematician, unfortunately, and I don't really master my own question. I have looked at all questions close to my question, but I could not understand anything because the level is much too high in mathematics.).
*Let's consider some generators g of a Lie group G. What are its elements ?
*If the group would not be a a Lie group, would the elements be different ones ?
*What is the connection between the generator of a Lie group, the element of the group, and the exponential function ?
*If the group is not a Lie group, is the expential disappearing ?