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Improved the statement.
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Anon
Anon
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Deformations Continuous families of finite subgroups of a Lie group

Suppose we have a continuous family of finite subgroups of a compact Lie group G. All the subgroups are necessarily isomorphic. Alternately, then all memberswe can say we have a continuous family of homomorphisms from a finite group K to G. Can we say that the images of all homomorphisms in this family areland in the same conjugacy class in G. This statement looks true to me, butCan I am havinghave a hard time proving it.reference or a proof?

Deformations of finite subgroups of a Lie group

Suppose we have a continuous family of finite subgroups of a compact Lie group G, then all members of the family are in the same conjugacy class. This statement looks true to me, but I am having a hard time proving it.

Continuous families of finite subgroups of a Lie group

Suppose we have a continuous family of finite subgroups of a compact Lie group G. All the subgroups are necessarily isomorphic. Alternately, we can say we have a continuous family of homomorphisms from a finite group K to G. Can we say that the images of all homomorphisms in this family land in the same conjugacy class in G. Can I have a reference or a proof?

Source Link
Anon
Anon
  • 778
  • 3
  • 11

Deformations of finite subgroups of a Lie group

Suppose we have a continuous family of finite subgroups of a compact Lie group G, then all members of the family are in the same conjugacy class. This statement looks true to me, but I am having a hard time proving it.