On the transposed Rao’s flag-transitive plane of order 49

摘要

Rao’s flag-transitive plane π of order 49 and π t , the plane obtained by transposing matrices of a representative set of π, has been studied. It is shown that π t is flag-transitive, π t is not isomorphic to π, and π t is obtained from π by replacement of a net of degree 25. Further, (1) the flag-transitive planes associated with 1-spread sets S _2b and S _2a in the classified list of translation planes of order 49 enumerated by Mathon et al, are respectively isomorphic to π and π t (2) The flag-transitive planes associated with the 1-spread sets of 0an* in the classified list of translation planes of order 49 enumerated by Charnes et al are isomorphic to π and π t in some order.