- #1

Mr Davis 97

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## Homework Statement

Show that a group with no proper nontrivial subgroups is cyclic.

## Homework Equations

## The Attempt at a Solution

If a group G has no proper nontrivial subgroups, then its only subgroups are ##\{e \}## and ##G##. Assume that G has at least two elements, and let ##a## be any element besides ##e##. Then ##a## generates a subgroup of ##G##, but ##G## has no proper nontrivial subgroups, which means that ##a## must generate ##G##, so ##G## is cyclic.

I feel that I am on the right track, but I also don't feel like I am being rigorous enough.