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This seems wrong. The conjugate closure should give the union of all conjugacy classes containing S, not the smallest normal subgroup containing S. For example, take S = { x } with x != 0, then the conjugate closure of S in (R,+) is just S. However S is not a subgroup of R. The statement would be true if S contained the identity however. — Preceding unsigned comment added by 76.204.99.5 ( talk) 22:12, 6 May 2011 (UTC) reply

• The conjugate closure is the subgroup GENERATED by S^G (thus written ${\displaystyle <S^{G}>}$). I made the same error about S={}. -- 72.226.86.106 ( talk) 16:50, 7 September 2014 (UTC) reply

As usual, the question is, what do independent reliable sources say? Deltahedron ( talk) 17:03, 7 September 2014 (UTC) reply