Infinite group

Prove that if , then is an infinite group.

Let . I am guessing I need to define a map but I don't know as what.

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Originally Posted by dwsmith

Prove that if , then is an infinite group.

Let . I am guessing I need to define a map but I don't know as what.

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for every integer , there is an obvious injection . so and thus .

Or you could note that it contains the transposition (n, n+1) for every natural number n.