Abstract

The spectrum ω (G) of a finite group G is the set of orders of elements of G. Let S be a simple exceptional group of type E6 or E7. We describe all finite groups G such that S ≤ G ≤ Aut S and ω (G) = ω (S) and completes the study of the recognition-by-spectrum problem for all simple exceptional groups of Lie type.

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