Abstract:
Groups are said to be isospectral if they have the same sets of element orders. Suppose that L is a finite simple linear or unitary group of dimension 4 over a field of odd characteristic. We prove that every finite group isospectral to L is an almost simple group with socle L.
Keywords:
simple classical group, element order, recognition by spectrum.
Citation:
M. A. Grechkoseeva, M. A. Zvezdina, “On recognition of l4(q) and u4(q) by spectrum”, Sibirsk. Mat. Zh., 61:6 (2020), 1300–1330; Siberian Math. J., 61:6 (2020), 1039–1065
This publication is cited in the following 7 articles:
M. A. Grechkoseeva, V. V. Panshin, “On Recognition of Low-Dimensional Linear and Unitary Groups by Spectrum”, Sib Math J, 65:5 (2024), 1074
M. A. Grechkoseeva, V. V. Panshin, “O raspoznavaemosti po spektru lineinykh i unitarnykh grupp nebolshoi razmernosti”, Sib. matem. zhurn., 65:5 (2024), 876–900
A. V. Vasilev, I. B. Gorshkov, “O gruppakh, ekstremalnykh otnositelno $p$-indeksa”, Algebra i logika, 62:1 (2023), 135–142
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
A. V. Vasil'ev, I. B. Gorshkov, “On p-Index Extremal Groups”, Algebra Logic, 62:1 (2023), 94
Peter J. Cameron, Natalia V. Maslova, “Criterion of unrecognizability of a finite group by its Gruenberg–Kegel graph”, Journal of Algebra, 607 (2022), 186
A. M. Staroletov, “Composition factors of the finite groups isospectral to simple classical groups”, Siberian Math. J., 62:2 (2021), 341–356
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