Algebra and Logic

, Volume 53, Issue 6, pp 433–449 | Cite as

Almost Recognizability by Spectrum of Simple Exceptional Groups of Lie Type

Article

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 isospectral to L is isomorphic to a group G squeezed between L and its automorphism group, i.e., L ≤ G ≤ AutL; in particular, up to isomorphism, there are only finitely many such groups. This assertion, together with a series of previously obtained results, implies that the same is true for every finite simple exceptional group except the group 3 D 4(2).

Keywords

finite simple groups exceptional groups of Lie type element orders prime graph recognition by spectrum 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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