Injectors with a central socle in a finite solvable group. (English) Zbl 1323.20015
This interesting and substantial paper is devoted to answer an open question of K. Doerk and T. Hawkes [Finite soluble groups. De Gruyter Expositions in Mathematics 4. Berlin: W. de Gruyter (1992; Zbl 0753.20001)] concerning the description of the injectors associated to the Fitting class \(\mathcal F^\pi\) of all finite soluble groups \(G\) whose \(\pi\)-socle, that is, the subgroup generated by the minimal normal \(\pi\)-subgroups of \(G\), \(\pi\) a set of primes, is contained in the centre of \(G\). The authors describe three types of constructions for the \(\mathcal F^\pi\)-injectors with the help of many nice auxiliary results. Some interesting examples are also presented.
Reviewer: Adolfo Ballester-Bolinches (Burjassot)
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.) |
Citations:
Zbl 0753.20001References:
[2] | Doerk, K.; Hawkes, T., Finite Soluble Groups (1992), de Gruyter · Zbl 0753.20001 |
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