In the answer to this question it seems that $$ \frac{O(n)/O(n-k)}{O(k)}\simeq \frac{O(n)}{O(n-k)\times O(k)} $$ should be obvious. How can I see this? Does this relation hold for $O(N)$ only or for more general Lie groups and subgroups too?
2026-03-28 05:22:37.1774675357
When does the isomorphism $G/H_1/H_2\simeq G/(H_1\times H_2)$ hold?
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