Residual properties of free groups. III (Q1802331)

The author proves in the affirmative the following conjecture, posed by W. Magnus and later by \textit{Yu. Gorchakov} and \textit{V. Levchuk} [Algebra Logika 9, No. 4, 415-421 (1970; Zbl 0221.20034)] and \textit{A. Lubotzky} [Proc. Am. Math. Soc. 98, No. 4, 583-585 (1986; Zbl 0632.20020)]: Let \(X\) be an infinite class of non-abelian finite simple groups. Then \(F_ 2\), the free group of rank 2, is residually \(X\). This conjecture was proved by \textit{R. Katz} and \textit{W. Magnus} [Commun. Pure Appl. Math. 22, 1-13 (1969; Zbl 0157.052)] in the special case where \(X\) contains an infinite set of alternating groups and by the author in the case where \(X\) contains an infinite set of classical groups of Lie type [part I, J. Algebra 160, No. 1, 16-41 (1993; Zbl 0805.20024), and part II, Commun. Algebra 20, No. 5, 1395-1425 (1992; Zbl 0751.20025)]. In the present paper the author proves the case where \(X\) contains an infinite set of exceptional groups of Lie type, proving thus the general case. See also the author's Ph.D. Thesis [Residuelle Eigenschaften freier Gruppen (Freiburg 1989; Zbl 0696.20026)].