The twenty-seven lines upon the cubic surface ... by Archibald Henderson.

HISTORICAL SUMMARY

7

Since Jordan's paper appeared in 1869, many writers have studied
the Galois group of the equation of the twenty-seven lines. Dickson*
has led in this investigation, publishing a number of papers on the
subject. Among those who have treated the problem of the twentyseven lines as a problem in substitution groups or Galoisian groups
may be mentioned Kiihnent, Weber, Pascal~, and Kasnerll. This
last paper is in close contact with the investigations of Moore~T and
Slaught"* on the cross-ratio group of Cremona transformations.
* Trans. American Math. Soc. Vol. II. (1901), pp. 137-138; Quart. Journ.
Vol. xxxiii. (1901), pp. 145-173; Bull. American lMath. Soc. Vol. viI. (1901),
p. 63 et sq.; Linear Groups, Ch. xiv. pp. 303-307, etc.
t Ueber die Galois'che Gruppe der Gleichung 27. Grades, von welcher die
Geraden auf der allgemeinen Fliche dritter Ordnung abhingen, Diss. Marburg.
1888.
+ "Ueber die Galois'che Gruppe der Gleichung 28. Grades, von welcher die
Doppeltangenten einer Curve vierter Ordnung abhangen," Math. Ann. Bd. xxII.
pp. 489-503.
~ " Groups of Substitutions connected with the Twenty-Seven Lines upon the
Cubic Surface," Annali di Matenmatica pura ed applicata, Vol. xx. (1892-3),
pp. 269 et seq.; Vol. xxi. (1893), pp. 85 et seq.
II American Journ. of Math. Vol. xxv. No. 2 (1903), pp. 107-122.
~ "The Cross-Ratio Group of n! Cremona Transformations of Order n- 3 in
Flat Space of n-3 Dimensions," American Journ. of Math. Vol. xxii. (1900),
p. 279.
** "The Cross-Ratio Group of 120 Quadratic Cremona Transformations of the
Plane," American Journ. of iMath. Vol. xxII. (1900), pp. 343-380.