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arXiv · 1806.07045

On recognition of symplectic and orthogonal groups of small dimensions by spectrum

M. A. Grechkoseeva·A. V. Vasil'ev·M. A. Zvezdina
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Abstract

We refer to the set of the orders of elements of a finite group as its spectrum and say that finite groups are isospectral if their spectra coincide. In the paper we determine all finite groups isospectral to the simple groups $S_6(q)$, $O_7(q)$, and $O_8^+(q)$. In particular, we prove that with just four exceptions, every such a finite group is an extension of the initial simple group by a (possibly trivial) field automorphism.

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M. A. Grechkoseeva, A. V. Vasil'ev, M. A. Zvezdina. 2018-06-19. On recognition of symplectic and orthogonal groups of small dimensions by spectrum. https://doi.org/10.1142/s021949881950230x

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