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We know that a group can not be written as a union of two proper subgroups and obiously a finite group can be written as a finite union of proper subgroups.So I want to ask if a infinite group be written as a finite union of proper subgroups?Moveover,Can a field be a finite union of proper subfields?

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    How are you going to write $\Bbb Z/3\Bbb Z$ or $\Bbb Z/4\Bbb Z$ as a union of **proper** subgroups?2012-08-15
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    Or $\mathbb Z$, for that matter.2012-08-15

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