On rank 5 projective planes (Q800635)

All known finite projective planes with a transitive collineation group G have been shown to be desarguesian. The conjecture that all such planes are desarguesian has been proved for low ranks \(\leq 4\) and under additional assumptions. The paper under review studies rank 5 planes P. The results are: If the order of P is \(n\neq 3\) then (i) G is a flag- transitive, (ii) G is solvable, (iii) P is non-desarguesian, (iv) n is a power of non-prime, \(n=m^ 4\) if n is odd, and \(n=m^ 2\) with \(m\equiv 0(mod 4)\) if n is even.