Strictly speaking it is redundant because as you have said a binary operation is defined on specific set S and must be closed  However this is interesting to think about  Strictly speaking I think the operation  on Z and  on Z really are the same operation since the elements in Z really are elements in Z  It is not the case that Z contains an isomorphic copy of Z where then the two  operations would really be different  So then I think that if you have a subgroup it actually isnt redundant to specify it must be closed under the given binary operation since it really is the same operation as that of the larger group  In any event I think the little blurb about closure is wordy and I would not object to its removal