Geodesic
A Note on Observable Subgroups of Linear Algebraic Groups and a Theorem of Chevalley
Journal of Lie theory, Tome 12 (2002) no. 1, pp. 301-304.

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Let H be an algebraic subgroup of a linear algebraic group G over an algebraically closed field K. We show that H is observable in G if and only if there exists a finite-dimensional rational G-module V and an element v of V such that H is the isotropy subgroup of v as well as the isotropy subgroup of the line Kv. Moreover, we give a similar result in the case where H contains a normal algebraic subgroup A which is observable in G. In this case, we deduce that H is observable in G whenever H/A has non non-trivial rational characters. We also give an example from complex analytic groups. 
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N. Nahlus . A Note on Observable Subgroups of Linear Algebraic Groups and a Theorem of Chevalley. Journal of Lie theory, Tome 12 (2002) no. 1, pp. 301-304. http://geodesic.mathdoc.fr/item/JLT_2002_12_1_JLT_2002_12_1_a15/