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Many of the basic concepts in this paper are defined in (2), and it will be useful to the reader if he is familiar with that paper. In it the concept of a loop transversal to a subgroup S of a group G is defined and discussed, where if G is a transitive permutation group and no explicit S is mentioned it is assumed that S is a point stabilizer. In (3) there appeared the following problem (P):
Let G be a transitive permutation group which is 2-closed.
(i) Is there a fixed-point-free transversal in G (i.e. to a point stabilizer)?
(ii) Is there a loop transversal in G?
Unfortunately a note was added in which it was falsely stated that the answer to both (i) and (ii) is yes.
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