Artin's conjecture on primitive roots, which was originally formulated
for multiplicative groups, has a natural analogue for elliptic curves.
In this survey talk, we will discuss the analogy and focus on "new" phenomena
such as the existence of "never-primitive" points.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246