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this video we will attempt to answer the question what is a free group to start with what would it mean for a group to be free the idea is that a group F would be free if its satisfied no other conditions than the group axioms so if its kind of a minimally constrained group so what properties might we expect in such a group we should expect that the non identity elements have infinite order this is because theres nothing in the group axioms themselves which say that they need to have finite order likewise we would expect free groups to be non abelian because requiring a group to be a billion means imposing an extra condition along with the group axioms the commutativity criterion of course though if we have two elements of the group F that are powers of a third element then that is a condition in which those elements would commute we would expect that all subgroups of free groups would be free this is because supposing we have a subgroup of this group F and it were not free that wo
