Geodesic
Unrecognizability by spectrum of finite simple orthogonal groups of~dimension nine
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 921-928

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The spectrum of a finite group is the set of its elements orders. A group $G$ is said to be unrecognizable by spectrum if there are infinitely many pairwise non-isomorphic finite groups having the same spectrum as $G$. We prove that the simple orthogonal group $O_9(q)$ has the same spectrum as $V\rtimes O_8^-(q)$ where $V$ is the natural 8-dimensional module of the simple orthogonal group $O_8^-(q)$, and in particular $O_9(q)$ is unrecognizable by spectrum. Note that for $q=2$, the result was proved earlier by Mazurov and Moghaddamfar.
Keywords: spectrum, element order, finite simple group.
Mots-clés : orthogonal group 
@article{SEMR_2014_11_a28,
     author = {M. A. Grechkoseeva and A. M. Staroletov},
     title = {Unrecognizability by spectrum of finite simple orthogonal groups of~dimension nine},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {921--928},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a28/}
}
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M. A. Grechkoseeva; A. M. Staroletov. Unrecognizability by spectrum of finite simple orthogonal groups of~dimension nine. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 921-928. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a28/