Why is the OST intuitively true? (Specially for the finite groups but also infinite groups) I understand the proof and the steps, but it is not obvious to me like let’s say Intermediate Value theorem.
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2Do any of these answers help? https://math.stackexchange.com/questions/242968 – Josh B. May 21 '19 at 11:52
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Does this answer your question? Intuition on the Orbit-Stabilizer Theorem – tryst with freedom Mar 11 '22 at 00:46
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The theorem is one of the many examples for The homomorphism theorem.
Many people see this as intuitive, as it is in many examples.
There are versions of this theorem for groups, rings, vector spaces, sets, etc., much more then just the few given on the Wikipedia page.
Dirk
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I'm not quite sure what you mean by the assertion in your first sentence, but for example the Orbit Stabilizer Theorem is not a corollary of the Homomorphism Theorem: the latter is concerned with normal subgroups, the former with arbitrary subgroups. – Lee Mosher May 21 '19 at 13:47
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1@LeeMosher No, I don't mean that it follows from the H. theorem. It is just a different version. The proof of the orbit stabilizer theorem and the homomorphism theorem are quite similar, just like the homomorphism theorem for vector spaces, sets, rings, etc. Therefore I said that it belongs together. Some textbooks introduce a very general case first (homomorphism theorem for maps between arbitrary sets, discussing the partition formed by preimages) and then everything else is just an application of that one. – Dirk May 21 '19 at 14:00