Let Gbe a connected algebraic group and Pa connected algebraic subgroup of G. If for any closed subgroup Hof Gwe have PH= HP, then Pis a normal subgroup of G(see [87]). Observe that for algebraic subgroups Pand Hof Gwith PH= HP, the group PHis an algebraic subgroup, too (see [45], 7.4 Corollary, p. 54).
For affine connected algebraic groups we can sharpen Theorem 1 in [87].
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Normality of Subgroups. In: Algebraic Groups and Lie Groups with Few Factors. Lecture Notes in Mathematics, vol 1944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78584-2_7
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DOI: https://doi.org/10.1007/978-3-540-78584-2_7
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