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.
Follow Math Help Forum on Facebook and Google+
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. 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.