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The spectrum of a finite group is the set of its elements orders. Groups are said to be isospectral if their spectra coincide. For every finite simple exceptional group L = E 7 (q), we prove that each finite group G isospectral to L is squeezed between L and its automorphism group, that is L ≤ G ≤ Aut L; in particular, there are only finitely many such groups. This assertion with a series of previously obtained results yields that the same is true for every finite simple exceptional group except the group 3 D 4 (2).

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