The factorizations of the finite exceptional groups of Lie type (Q1085270)

In this paper the factorizations \(G=AB\) of exceptional finite simple groups G of Lie type are determined. It is shown, that only \(G_ 2(q)\) and \(F_ 4(q)\) have factorizations and these factorizations are given explicitly. By a former result of two of the authors [Preprint, Univ. Cambridge (1985)] one knows the structure of A if one assumes \(| A| \geq | B|\). Secondly, if G is defined over GF(q), one looks for primitive divisors of \(q^ a-1\) where a is ''big'' and observes that such primes occur in \(| B|\). These facts then can be played off against each other effectively to obtain the result.