On maximal nilpotent \(\pi\)-subgroups. (English) Zbl 1084.20501
Campbell, C.M.(ed.) et al., Groups St. Andrews 2001 in Oxford. Selected papers from the international conference, Oxford, UK, August 5–18, 2001. Vol. II. Cambridge: Cambridge University Press (ISBN 0-521-53740-1/pbk). London Mathematical Society Lecture Note Series 305, 405-411 (2003).
Summary: We prove the existence of injectors in any group for the class of nilpotent \(\pi\)-groups. We also prove that in a soluble group \(G\), the number of conjugacy classes of \(G/O_\pi({\mathbf F}(G))\) is bounded by the index of an injector of this class.
For the entire collection see [Zbl 1074.20501].
For the entire collection see [Zbl 1074.20501].
MSC:
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20D25 | Special subgroups (Frattini, Fitting, etc.) |
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
