Abstract: In this article a class of subgroups of a finite group, called Q-injectors, is introduced. If G is soluble, the Q-injectors are precisely the injectors of the Fitting sets. A characterization of nilpotent Q-injectors is given as well as a sufficient condition for the solubility of a finite group G, in terms of Q-injectors, which generalizes a well known result.
A characterization of nilpotent injectors in finite groups / A.L.Gilotti; L.Serena. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 39:(2011), pp. 4118-4127. [10.1080/00927872.2010.519365]
A characterization of nilpotent injectors in finite groups
GILOTTI, ANNA LUISA;SERENA, LUIGI
2011
Abstract
Abstract: In this article a class of subgroups of a finite group, called Q-injectors, is introduced. If G is soluble, the Q-injectors are precisely the injectors of the Fitting sets. A characterization of nilpotent Q-injectors is given as well as a sufficient condition for the solubility of a finite group G, in terms of Q-injectors, which generalizes a well known result.
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