‘On projective planes of type (6, m)’

Abstract

Alan Rahilly has pointed out to me that the proof of the Theorem in my paper (2) is incomplete. This correction will now complete it. I would also like to acknowledge here that the results which are actually established in (2) can also be found in the paper (5) by Praeger and Rahilly.The trouble was in the proof of Proposition 2. Although the group G has a subgroup H1 which intersects each of its conjugates trivially, the same is not necessarily true of the image H1N/N of H1 in the 2-transitive representation G/N of G referred to in the paper. A theorem of M. E. O'Nan from (4) was used along with Proposition 2 to establish my theorem. What should have been done was to look at O'Nan's results more deeply and combine them with other results. Here is the way that it is done.There is nothing actually wrong with the argument in my paper; it is just that it is not complete. The proof here will continue the argument of (2) using the notations established there.