Abstract:
The spectrum of a finite group is the set of the orders of its elements. We consider the problem that arises within the framework of recognition of finite simple groups by spectrum: Determine all finite almost simple groups having the same spectrum as its socle. This problem was solved for all almost simple groups with exception of the case that the socle is a simple even-dimensional orthogonal group over a field of odd characteristic. Here we address this remaining case and determine the almost simple groups in question.
Also we prove that there are infinitely many pairwise nonisomorphic finite groups having the same spectrum as the simple 8-dimensional symplectic group over a field of characteristic other than 7.
Keywords:
almost simple group, orders of elements, recognition by spectrum, quasirecognition.
\Bibitem{Gre18}
\by M.~A.~Grechkoseeva
\paper On spectra of almost simple extensions of even-dimensional orthogonal groups
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 4
\pages 791--813
\mathnet{http://mi.mathnet.ru/smj3010}
\crossref{https://doi.org/10.17377/smzh.2018.59.405}
\elib{https://elibrary.ru/item.asp?id=35736203}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 4
\pages 623--640
\crossref{https://doi.org/10.1134/S0037446618040055}
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Linking options:
https://www.mathnet.ru/eng/smj3010
https://www.mathnet.ru/eng/smj/v59/i4/p791
This publication is cited in the following 9 articles:
M. A. Grechkoseeva, “Raspoznavaemost grupp PSp8(7m) po mnozhestvu poryadkov elementov”, Matem. zametki, 117:4 (2025), 494–504
Alexander A. Buturlakin, Maria A. Grechkoseeva, “The spectra of almost simple groups with socle E
7
(q)”, Communications in Algebra, 52:1 (2024), 208
Maria A. Grechkoseeva, Victor D. Mazurov, Wujie Shi, Andrey V. Vasil'ev, Nanying Yang, “Finite Groups Isospectral to Simple Groups”, Commun. Math. Stat., 11:2 (2023), 169
Peter J. Cameron, Natalia V. Maslova, “Criterion of unrecognizability of a finite group by its Gruenberg–Kegel graph”, Journal of Algebra, 607 (2022), 186
Maria A. Grechkoseeva, Andrey V. Vasil'ev, “On the prime graph of a finite group with unique nonabelian composition factor”, Communications in Algebra, 50:8 (2022), 3447
N. V. Maslova, “2020 Ural Workshop on Group Theory and Combinatorics”, Tr. IMM UrO RAN, 27, no. 1, 2021, 273–282
M. A. Grechkoseeva, M. A. Zvezdina, “On recognition of l4(q) and u4(q) by spectrum”, Siberian Math. J., 61:6 (2020), 1039–1065
M. A. Grechkoseeva, A. V. Vasil'ev, M. A. Zvezdina, “Recognition of symplectic and orthogonal groups of small dimensions by spectrum”, J. Algebra. Appl., 18:12 (2019), 1950230
Lytkin Yu.V., “On Finite Groups Isospectral to the Simple Groups S-4(Q)”, Sib. Electron. Math. Rep., 15 (2018), 570–584
Citation in format AMSBIB
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