On injectors of finite groups. (English) Zbl 1281.20022
Summary: If \(\mathcal F\) is a non-empty Fitting class, \(\pi=\pi(\mathcal F)\) and \(G\) a group such that every chief factor of \(G/G_{\mathcal F}\) is an \(C_\pi^s\)-group. Then \(G\) has at least one \(\mathcal F\)-injector. This result is used to resolve an open problem and generalize some known results.
MSC:
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
| 20D25 | Special subgroups (Frattini, Fitting, etc.) |
