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Recognition of the simple groups \(U_3(q)\) by element orders. (Russian, English) Zbl 1117.20010

Algebra Logika 45, No. 2, 185-202 (2006); translation in Algebra Logic 45, No. 2, 106-116 (2006).
Summary: An exhaustive solution is given to the recognition-by-spectrum problem for finite, simple, three-dimensional unitary groups. For every such group, the number of non-isomorphic, finite, isospectral groups is determined. In particular, a new counterexample to Problem 13.63 in The Kourovka notebook [V. D. Mazurov and E. I. Khukhro (eds.), Unsolved problems in group theory, Novosibirsk (2002; Zbl 0999.20001)] is furnished.

MSC:

20D06 Simple groups: alternating groups and groups of Lie type
20D60 Arithmetic and combinatorial problems involving abstract finite groups

Citations:

Zbl 0999.20001
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