On R. Griess' ''Friendly giant''
This paper in an improvement of a part of the construction of the Fischer-Griess simple group F given by the author [in Sémin. Bourbaki, 36e année, 1983/84, Exp. No.620, Astérisque 121-122, 105-122 (1985; reviewed above)]. As in the original contruction by \textit{R. Griess} [Invent. Math. 69, 1-102 (1982; Zbl 0498.20013)] the 196883-dimensional irreducible representation of F over \({\mathbb{Q}}\) is the starting point for the construction of F. The author begins with a 196883-dimensional representation of C which is an extension of an extraspecial group of order \(2^{1+24}\) by \(\cdot 1\). He shows that there is an algebra multiplication and a bilinear form on this module B which are invariant under C. By elementary means the author proves as his main result: \(\tilde F=Aut(B)\) is finite and \(C=C_{\tilde F}(z)\) for \(Z(C)=<z>\). Once one has established that \(\tilde F\neq C\) one can quote a result of \textit{S. D. Smith} [J. Algebra 58, 251-281 (1979; Zbl 0411.20009)] to obtain \(\tilde F\simeq F\).
scientific article; zbMATH DE number 3873578