Injectors of locally soluble FC-groups. (English) Zbl 0606.20032
For a Fitting set F of a locally soluble FC-group, the existence and local conjugacy of F-injectors is established. In particular, the locally nilpotent injectors are described. Normally embedded subgroups of locally soluble FC-groups are characterized in terms of Fischer sets.
MSC:
| 20F24 | FC-groups and their generalizations |
| 20F19 | Generalizations of solvable and nilpotent groups |
| 20E07 | Subgroup theorems; subgroup growth |
| 20F17 | Formations of groups, Fitting classes |
Keywords:
Fitting set; injectors; locally nilpotent injectors; locally soluble FC- groups; Fischer setsReferences:
| [1] | Beidleman, J. C., Karbe, M. J.: On normally embedded subgroups of locally soluble FC-groups. Glasgow Math. J.28, 153-159 (1986). · Zbl 0593.20048 · doi:10.1017/S0017089500006479 |
| [2] | Fischer, B., Gaschütz, W., Hartley, B.: Injektoren endlicher auflösbarer Gruppen. Math. Z.102, 337-339 (1967). · Zbl 0183.02902 · doi:10.1007/BF01111070 |
| [3] | Hartley, B.: On Fischer’s dualization of formation theory. Proc. London Math. Soc. (3)19, 193-207 (1969). · Zbl 0169.34201 · doi:10.1112/plms/s3-19.2.193 |
| [4] | Tomkinson, M. J.:F-injectors of locally soluble FC-groups. Glasgow Math. J.10, 130-136 (1969). · Zbl 0185.05401 · doi:10.1017/S0017089500000689 |
| [5] | Tomkinson, M. J.: FC-groups. Boston-London-Melbourne: Pitman. 1984. · Zbl 0547.20031 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
