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nontrivial subgroups, finitude or infinitude

Source: LIMIT 2019 CCS1 P5

April 28, 2021

group theoryabstract algebra

Problem Statement

Let

G=(S^1,\cdot)

be a group. Then its nontrivial subgroups

<span class='latex-bold'>(A)</span>~\text{are necessarily finite}

<span class='latex-bold'>(B)</span>~\text{can be infinite}

<span class='latex-bold'>(C)</span>~\text{can be dense in }S^1

<span class='latex-bold'>(D)</span>~\text{None of the above}