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The growth of a subset of a group

The answer is yes. In fact, it can be proved in a totally elementary way. Because $1 \in S^2 \subset gS$, we have $g^{-1} \in S$ and thus $g \in S$. Then since $S^2 \subset gS \subset S^2$, it follo …
Dongryul Kim's user avatar
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