Iranzo, M. J.; Pérez Monasor, Francisco \({\mathcal F}\)-constraint with respect to a Fitting class. (English) Zbl 0571.20012 Arch. Math. 46, 205-210 (1986). Let \({\mathcal F}\) be a Fitting class and \(\pi =char {\mathcal F}=\{p|\) \(C_ p\in {\mathcal F}\}\), we say that a group G is \({\mathcal F}\)-constrained when \(C_{\bar G}(\bar G_{{\mathcal F}})\leq G_{{\mathcal F}}\), where \(\bar G=G/O_{\pi '}(G)\). We denote by \({\mathcal X}_{{\mathcal F}}\) the class of \({\mathcal F}\)-constrained groups. In this paper we prove the following results: i) \({\mathcal X}_{{\mathcal F}}\) is a Fitting class. ii) If \({\mathcal N}\subseteq {\mathcal F}\subseteq \tilde N\), then all \({\mathcal X}_{{\mathcal F}}\)-groups possess a unique conjugacy class of \({\mathcal F}\)-injectors. We analyze also the relations between two Fitting classes \({\mathcal F}\) and \({\mathcal H}\) such that \({\mathcal X}_{{\mathcal F}}={\mathcal X}_{{\mathcal H}}\). Cited in 7 Documents MSC: 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure Keywords:Fitting class; \({\mathcal F}\)-constrained groups; conjugacy class of \({\mathcal F}\)-injectors PDFBibTeX XMLCite \textit{M. J. Iranzo} and \textit{F. Pérez Monasor}, Arch. Math. 46, 205--210 (1986; Zbl 0571.20012) Full Text: DOI References: [1] D. Blessenohl undH. Laue, Fittingklassen endlicher Gruppen in denen gewisse Haupfaktoren einfach sind. J. Algebra56, 516-532 (1979). · Zbl 0416.20015 · doi:10.1016/0021-8693(79)90355-7 [2] T.Gagen, Topics in Finite Groups. Cambridge 1976. · Zbl 0324.20013 [3] D. Gorenstein andJ. Walter, The ?-layer of a finite group. Illinois J. Math.15, 555-564 (1971). · Zbl 0244.20017 [4] B.Huppert, Endliche Gruppen I. Berlin 1967. · Zbl 0217.07201 [5] M. J.Iranzo and F.Perez Monasor, ?-constraint of the automorphism group of a finite group. Rend. Sem. Mat. Univ. Padova (to appear). [6] A. Mann, Injectors and normal subgroups of finite groups. Israel J. Math.9, 554-558 (1971). · Zbl 0228.20005 · doi:10.1007/BF02771470 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.