On the existence of certain generalized Moore geometries. V (Q908929)

This is a continuation of the series of papers by \textit{C. Roos} and \textit{A. J. van Zanten} on the existence of generalized Moore geometries of type \(GM_ m(s,t,s+1)\) [see ibid. 51, 179-190 (1984; Zbl 0547.05021), ibid. 51, 277-282 (1984; Zbl 0547.05022), ibid. 58, 275-283 (1986; Zbl 0594.05020), ibid. 62, 139-144 (1986; Zbl 0613.05016]. In the present paper the nonexistence is proved if \(m=5\), which combined with previous results yields that \(GM_ m(s,t,s+1)\) cannot exist if \(m\geq 4\) and st\(\geq 2\).