Minimal Extensions of Algebraic Groups and Linear Independence, Original Research Article

We introduce the notion of a minimal extension of t-groups. Linear independence of the coordinates of the logarithm of an algebraic point in a minimal extension of t-groups follows naturally from linear independence of the coordinates of the image in the tangent space of the base t-group. We illustrate this principle through a leisurely parade of examples. In particular, we establish a general theorem about divided derivatives for t-modules. Minimal extensions turn out to correspond to Frattini covers for t-groups.