Article ID Journal Published Year Pages File Type
5771773 Journal of Algebra 2017 28 Pages PDF
Abstract

For a finite smooth algebraic group F over a field k and a smooth algebraic group G¯ over the separable closure of k, we define the notion of F-kernel in G¯ and we associate to it a set of nonabelian 2-cohomology. We use this to study extensions of F by an arbitrary smooth k-group G. We show in particular that any such extension comes from an extension of finite k-groups when k is perfect and we give explicit bounds on the order of these finite groups when G is linear. We prove moreover some finiteness results on these sets.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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