THE CORRELATIONS OF FINITE DESARGUESIAN PLANES OF SQUARE ORDER DEFINED BY UPPER TRIANGULAR MATRICES WITH FIVE NONZERO ENTRIES
The present article is the tenth and last in the series of papers devoted to the classification of correlations of finite Desarguesian planes.
The following symbols shall be used, in agreement with the previous articles devoted to the classification of correlations:
q:a prime power (no distinction is being made between odd or even prime powers)
F:the finite field
F¢:the subfield of F
F²:the subfield of F
w:a primitive root of F
*:a matrix entry which may or may not be zero
*¢:a nonzero matrix entry
AP:absolute point of a correlation
NAP:nonabsolute point of a correlation
SQ:the subset of F comprising the squares;
NS:the subset of F comprising the nonsquares
Q:the subset of F comprising the nonvanishing powers
ZQ:the subset of F comprising the nonvanishing powers
TQ:the subset of F comprising the powers
over F
over F.
companion automorphism, absolute set, pseudo-correlations, full secant, short secant.
