Quasinormal Fitting classes of finite groups
| Autor: | Anna V. Martsinkevich |
|---|---|
| Jazyk: | Belarusian<br />English<br />Russian |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Журнал Белорусского государственного университета: Математика, информатика, Iss 2, Pp 18-26 (2019) |
| Druh dokumentu: | article |
| ISSN: | 2520-6508 2617-3956 |
| DOI: | 10.33581/2520-6508-2019-2-18-26 |
| Popis: | Let P be the set of all primes, Zn a cyclic group of order n and X wr Zn the regular wreath product of the group X with Zn. A Fitting class F is said to be X-quasinormal (or quasinormal in a class of groups X ) if F ⊆ X, p is a prime, groups G ∈ F and G wr Zp ∈ X, then there exists a natural number m such that G m wr Zp ∈ F. If X is the class of all soluble groups, then F is normal Fitting class. In this paper we generalize the well-known theorem of Blessenohl and Gaschütz in the theory of normal Fitting classes. It is proved, that the intersection of any set of nontrivial X-quasinormal Fitting classes is a nontrivial X-quasinormal Fitting class. In particular, there exists the smallest nontrivial X-quasinormal Fitting class. We confirm a generalized version of the Lockett conjecture (in particular, the Lockett conjecture) about the structure of a Fitting class for the case of X-quasinormal classes, where X is a local Fitting class of partially soluble groups. |
| Databáze: | Directory of Open Access Journals |
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