Talk:Examples of groups

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Under "the set of maps":

"And there is a map i such that i(x)=e where e is the unit element of G. The map i makes all the functions f in M(S,G) such that if=fi=f, or i is the unit element of M(S,G)."

Shouldn't the identity function i(x) = x ???

Take, for example, the group of nonzero rationals under multiplication. Then e is 1. And if we let i(x) = 1, we do not get if = fi = f.

This seems pretty undeniable, but I'm just now taking abstract algebra, so maybe I'm misunderstanding the situation. I don't want to presume to correct whoever wrote this without the consensus of other readers.