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Title: | Finite π-groups with normal injectors |
Authors: | Vorob’ev, N. T. Martsinkevich, A. V. |
Keywords: | Fitting class π-normal Fitting class product of Fitting classes lattice join of Fitting classes |
Issue Date: | 2015 |
Publisher: | Pleiades Publishing, Ltd. |
Citation: | Vorob’ev, N. T. Finite π-groups with normal injectors / N. T Vorob’ev, A. V. Martsinkevich // Siberian Mathematical Journal. – 2015. – Vol. 56, № 4. – P. 624–630. |
Series/Report no.: | Siberian Mathematical Journal;Vol. 56, № 4 |
Abstract: | Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F = (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. |
URI: | https://rep.vsu.by/handle/123456789/33402 |
ISSN: | 0037-4466 |
Appears in Collections: | Научные публикации (2015) |
Files in This Item:
File | Description | Size | Format | |
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Finite π-groups with normal injectors_2015_56_04.pdf | 222.86 kB | Adobe PDF | View/Open |
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