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Minimal Extensions of Algebraic Groups and Linear Independence

✍ Scribed by W.Dale Brownawell

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
164 KB
Volume
90
Category
Article
ISSN
0022-314X

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✦ Synopsis

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.

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