Point sets and allied Cremona groups. III
Arthur B. Coble · Transactions of the American Mathematical Society · 1917
These Transactions, vol.17 (1916).|| That an equation of degree 27 for the lines of a cubic surface could be solved by hyperelliptic modular functions was first pointed out by Klein in a letter to Hermite, Journal de mathématiques, ser.4, vol. 4 (1888), p. 169.His suggestions were elaborated by Witting, Mathematische Annalen, vol.29 (1887), p. 167; by Maschke, ibid., vol.33 (1889), p. 317; and by Burkhardt, Grundzüge einer allgemeinen Systematik der hyperelliptischen Functionen I. Ordnung, ibid., vol.35 (1890), p. 198, vol.38 (1891), p. 161, and vol.41 (1893), p. 313.The latter articles are referred to as BI, BII, and Bill.Since Maschke and Burkhardt respectively have determined complete systems for the so-called "group of the Z's " and "group of the 7's " we shall indicate these groups and the associated form problems by attaching their names.* Sousley, American Journal of Mathematics, vol.38 (1916).* Such a subgroup (one of 36) is generated by the elements ( 12 ) ■ I, ■ ■ • , ( 56 ) ■ / of r6,2.t Coble, An invariant condition for certain aulomorphic algebraic forms, American Journal of Mathematics, vol.28 (1906).* Since G2592o is simple it can be enlarged to a correlation group in only one way.Trans.Am.Math.Soc.Ï3* As to the difficulty of the reduction here indicated cf.Bill, p. 339*.The use of kleinian forms to determine covariant points is illustrated in the article: Coble, Reduction of the sextic equation to the Valentiner form problem, Mat h_e matische Annalen, vol.70 (1911), p. 337.