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The factorizations of the finite exceptional groups of Lie type. (English) Zbl 0607.20012
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.
Reviewer: U.Dempwolff

##### MSC:
 20D40 Products of subgroups of abstract finite groups 20D06 Simple groups: alternating groups and groups of Lie type 20G40 Linear algebraic groups over finite fields
##### Keywords:
factorizations; finite simple groups
Full Text:
##### References:
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