Linear Algebraic Groups
James E. Humphreys
an exercise on p.57
A closed subset of a linear algebraic group
which contains e (the identity element) and
is closed under taking products is a subgroup.
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2
Say the group is G, and the closed subset is X. Consider the right regular
representation of G in K[G]. Take a finite dimensional G-invariant subspace
V of K[G] such that W=V\cap I(X) generates I(X). Let H be the stabilizer of
W in G. Then H is a subgroup. It is not difficult to show that H=X.
【在 f******h 的大作中提到】 : Linear Algebraic Groups : James E. Humphreys : an exercise on p.57 : A closed subset of a linear algebraic group : which contains e (the identity element) and : is closed under taking products is a subgroup.
