Tuesday, 1 October 2013

Examples of uncountable subgroups, but with countably many cosets.

Examples of uncountable subgroups, but with countably many cosets.

My question is pretty much as stated in the title: what examples are there
(or does there exist) uncountable subgroups of uncountable order, but
which give countably-infinite many cosets. I can only think of examples in
the other direction (countable subgroups giving uncountably-many cosets).

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