Orthogonal group is finite-dominating in general linear group over any real-closed field

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Template:Finite-dominating subgroup statement

This article gives the statement, and possibly proof, of a particular subgroup or type of subgroup (namely, Orthogonal group (?)) satisfying a particular subgroup property (namely, Finite-dominating subgroup (?)) in a particular group or type of group (namely, General linear group (?)).

Definition

Let k be a real-closed field, for instance, k = \R, and n be any natural number. Then, any finite subgroup of the general linear group GL(n,k) is conjugate in GL(n,k) to a subgroup of the orthogonal group O(n,k).

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