A characterization of finite simple groups by the orders of solvable subgroups.
The authors prove that if a finite group \(G\) and a finite simple group \(S\) have the same sets of all orders of solvable subgroups, then \(G\) is isomorphic to \(S\), or \(G\) and \(S\) are isomorphic to \(B_n(q)\), \(C_n(q)\), where \(n\geq 3\) and \(q\) is odd. Since \textit{N. Ahanjideh} and \textit{A. Iranmanesh} prove a theorem on the difference of orders of solvable subgroups between \(B_n(q)\) and \(C_n(q)\) [On the difference between orders of solvable subgroups of the nonisomorphic simple groups \(B_n(q)\) and \(C_n(q)\) (manuscript)], the conjecture put forward by \textit{S. Abe} and \textit{N. Iiyori}, [Hokkaido Math. J. 29, No. 2, 391-407 (2000; Zbl 0965.20008)], is proved.
scientific article; zbMATH DE number 5189100
scientific article