On the head characters of the Monster simple group. (English) Zbl 0591.20023
Finite groups - coming of age, Proc. CMS Conf., Montreal/Que. 1982, Contemp. Math. 45, 303-313 (1985).
[For the entire collection see Zbl 0565.00006.]
From the author’s introduction: ”This article will serve to review and update the report of P. Fong [Proc. Symp. Pure Math. 37, 557-559 (1980; Zbl 0448.20019)] at the 1979 Santa Cruz meeting. We describe a computer calculation of A. O. L. Atkin, P. Fong, and S. Smith to establish the conjecture of Thompson and Conway about the Head characters of the Monster - indicating how the result is reduced to certain assertions about coefficients of modular functions, which are known to hold at least asymptotically.” The author also gives a description of Thompson’s reformulation of Brauer’s characterization of characters.
From the author’s introduction: ”This article will serve to review and update the report of P. Fong [Proc. Symp. Pure Math. 37, 557-559 (1980; Zbl 0448.20019)] at the 1979 Santa Cruz meeting. We describe a computer calculation of A. O. L. Atkin, P. Fong, and S. Smith to establish the conjecture of Thompson and Conway about the Head characters of the Monster - indicating how the result is reduced to certain assertions about coefficients of modular functions, which are known to hold at least asymptotically.” The author also gives a description of Thompson’s reformulation of Brauer’s characterization of characters.
Reviewer: D.Held
MSC:
| 20D08 | Simple groups: sporadic groups |
| 11F03 | Modular and automorphic functions |
| 20C15 | Ordinary representations and characters |
| 20C20 | Modular representations and characters |
| 11F11 | Holomorphic modular forms of integral weight |
