Almost Recognizability by Spectrum of Simple Exceptional Groups of Lie Type

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...

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Bibliographic Details
Published in:Algebra and logic 2015-01, Vol.53 (6), p.433-449
Main Authors: Vasil’ev, A. V., Staroletov, A. M.
Format: Article
Language:English
Subjects:
Algebra
Finite groups
Isomorphisms (Mathematics)
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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Summary: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 ≤ Aut L ; 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) .
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-015-9305-1