Epimorphic subgroups of algebraic groups

In this note, we show that the epimorphic subgroups of an algebraic group are exactly the pull-backs of the epimorphic subgroups of its affinization. We also obtain epimorphicity criteria for subgroups of affine algebraic groups, which generalize a result of Bien and Borel. Moreover, we extend the affinization theorem for algebraic groups to homogeneous spaces.

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Received 28 June 2016

Accepted 2 January 2017

Published 29 January 2018