Some language purists would maintain that each other refers to two people or things and one another to more than two, but the general opinion now is that the two expressions are interchangeable. However, one another is often seen as being more formal.

The two animals stared fiercely at each other.
We have known one another for years.

The genitive is used with an apostrophe plus s:

They compared each other’s (one another’s) notes.

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