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Epimorphic subgroups of linear algebraic groups. I. (Sous-groupes épimorphiques de groupes linéaires algébriques. I.) (French) Zbl 0767.20017
Summary: A closed subgroup \(H\) of a connected linear algebraic group \(G\) is said to be epimorphic if any morphism of \(G\) into an algebraic group is determined by its restriction to \(H\). This note is devoted to general properties and examples of epimorphic subgroups. We also give partial results pertaining to a finiteness property of induced representations, and we formulate a general conjecture. A subsequent note will relate epimorphic subgroups to problems of finite generation of invariants, compactifications and multiplicities of representations.

20G15 Linear algebraic groups over arbitrary fields
20E36 Automorphisms of infinite groups
20G05 Representation theory for linear algebraic groups
20E07 Subgroup theorems; subgroup growth