New characterizations of σ-nilpotent finite groups

Let σ = { π i ∣ i ∈ I } be a partition of the set of all primes. We characterize the class of all σ -nilpotent groups as a hereditary formation F that contains every group G all whose Sylow subgroups are K - F -subnormal in their product with the generalized Fitting subgroup F ∗ ( G ) .

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Bibliographic Details
Published inRicerche di matematica Vol. 73; no. 1; pp. 611 - 618
Main Authors Viachaslau, I Murashka, F Vasil’ev Alexander
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2024
Springer Nature B.V
Subjects
Algebra
Analysis
Geometry
Group theory
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
Subgroups
Secondary 20F17
Primary 20D25
Finite group
subnormal subgroup
20F19
Generalized Fitting subgroup
Hereditary formation
nilpotent group
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Summary:Let σ = { π i ∣ i ∈ I } be a partition of the set of all primes. We characterize the class of all σ -nilpotent groups as a hereditary formation F that contains every group G all whose Sylow subgroups are K - F -subnormal in their product with the generalized Fitting subgroup F ∗ ( G ) .
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-021-00627-8