9.43 (1984)

a) The group $G$ described in the solution of problem 8.73 enables us to construct a projective plane of order 3 in which the lines are the elements of any conjugacy class of subgroups of order $2 \cdot 5 \cdot 7 \cdot 11$ together with four lines added in a natural way. In a similar way, we can construct a projective plane of order $p^n$ for any prime $p$ and any positive integer $n$. Does the resulting projective plane have the Galois property?

b) The group $G$ indicated in (N. D. Podufalov, Abstracts of the 9th All–Union Symp. on Group Theory, Moscow, 1984, 113–114 (Russian)) allows us to construct a projective plane of order 3: one can take as lines any class of subgroups of order $2 \cdot 5 \cdot 11 \cdot 17$ conjugate under $S$ and add four more lines in a natural way. In a similar way, one can construct projective planes of order $p^n$ for any prime $p$ and any natural $n$. Could this method be adapted for constructing new planes?