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A group satisfying the conditions of the previous theorem is called unipotent k-group?.
Unipotent groups correspond by duality to connected formal -groups.
The category of affine commutative unipotent groups form a thick subcategory of which is stable under limits.
The following theorem is the dual to the theorem of the previos chapter.
An affine group is in a unique way an extension of a unipotent group by a multiplicative group.
This extension splits if is perfect.
The category of finite commutative -groups splits as a product of four subcategories: , , , .
The categories and are dual to each other.
The categories and are selfdual.
Let , then Then .
Let , let be algebraically closed. Then any commutative finite -group is an extension of copies of , and where is prime.
If is a prime and is a finite commutative -group, then for large iff is a power of .