[SOLVED] smallest normal subgroup 1. The problem statement, all variables and given/known data Given any subset S of a group G, show that it makes sense to speak of the smallest normal subgroup that contains S. Hint: Use the fact that an intersection of normal subgroups of a group G is again a normal subgroup of G. 2. Relevant equations 3. The attempt at a solution The hint makes the proof easy when G is finite. When G is infinite, I do not think that the result holds since the intersection, for example of two alpha_0 sets, can be the same cardinality of the original sets. Can someone confirm?