ABSTRACT
Let E denote the elation group of order q2 with axis x = 0 of the associated Desarguesian plane 1 . Note that
E =
* u;t =
2664 1 0 u+ 1t 1t 0 1 t u 0 0 1 0 0 0 0 1
3775 ;u; t 2 GF (q) + .
Let 2 and 3 denote two conical ‡ock spreads of odd order distinct from 1 in PG(3; q) that share precisely R0 with 1, which may be represented as:
i =
x = 0; y = x
u+ gi(t) fi(t)
t u
;u; t 2 GF (q)
;
i = 2; 3
and assume that for any given t0,
gi(t0) = 1t0;
fi(t0) = 1t0
implies t0 = 0 (this condition simply is that the given spreads share exactly R0 with 1): Note that either of these spreads could also be Desarguesian. Let E denote the subgroup of E that …xes R0 and hence is a collineation group of 1, and i, for i = 1; 2.
