Recognition of finite groups by a set of orders of their elements. (English. Russian original) Zbl 0917.20021
Algebra Logika 37, No. 6, 651-666 (1998); translation in Algebra Logic 37, No. 6, 371-379 (1998).
The main result of the article is as follows: The almost simple groups \(\text{PGL}_n(q)\) are unrecognizable for an infinite set of pairs \((n,q)\). Some results are also obtained about recognition of some particular groups. Namely, it is shown that the simple group \(S_4(7)\) is recognizable, while the groups \(A_{10}\), \(U_3(3)\), \(U_3(5)\), \(U_3(7)\), \(U_4(2)\), and \(U_5(2)\) are unrecognizable.
Reviewer: M.F.Murzina (Novosibirsk)
MSC:
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
| 20D06 | Simple groups: alternating groups and groups of Lie type |
