Abstract
In this paper we prove that in positive characteristics normal embeddings of connected reductive groups are Frobenius split. As a consequence, they have rational singularities and are thus Cohen-Macaulay varieties. As an application, we study the particular case of reductive monoids, which are affine embeddings of their unit group. In particular, we show that the algebra of regular functions of a normal irreducible reductive monoid M has a good filtration for the action of the unit group of M.
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