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Factorizations of fitting classes
Frontiers of Mathematics in China, 2012This paper focuses on the theory of Fitting classes of finite groups. A class \(\mathcal F\) of groups is called a Fitting class if every normal subgroup of an \(\mathcal F\)-group is an \(\mathcal F\)-group and if the product of two normal \(\mathcal F\)-subgroups of a group is again an \(\mathcal F\)-group.
Nanying, Yang +2 more
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Dualpronormality and fitting classes [PDF]
Communications in Algebra, 1998 In this paper we extend dualpronormality to an arbitrary Fitting class, introducing the notion of F-dualpronormality, and investigate groups having a structure of F-dualpronormal subgroups which is particularly rich or particularly poor.
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2023
In their quest to provide a wholistic education, schools are providing more in-house source services to students. Specifically, schools are responding to the aftermath of childhood trauma and/or toxic stress, which commonly manifest as negative behaviors and emotional dysregulation in the classroom.
Dana C. Branson, Noah R. Branson
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In their quest to provide a wholistic education, schools are providing more in-house source services to students. Specifically, schools are responding to the aftermath of childhood trauma and/or toxic stress, which commonly manifest as negative behaviors and emotional dysregulation in the classroom.
Dana C. Branson, Noah R. Branson
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On normal Fitting classes [PDF]
Archiv der Mathematik, 1998 The paper contains some characterizations of normal Fitting classes. Let \(\mathcal F\) be a Fitting class of finite soluble groups. It is proved that \(\mathcal F\) is a normal Fitting class if and only if every \(\mathcal F\)-dualpronormal subgroup has respectively one of the following embedding properties: normal, subnormal, pronormal, normally ...
D'ANIELLO A +2 more
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Annali di Matematica Pura ed Applicata, 1990
A Fitting class construction is presented which has affinities with that of \textit{R. S. Dark} [Math. Z. 127, 145-156 (1972; Zbl 0226.20013)]. All groups considered are finite and soluble. Let \(p\), \(q\), \(r\) be primes. The author defines \({\mathcal M}\) as the class of groups of the form \(ABU\), where \(A\), \(B\) and \(U\) are nontrivial ...
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A Fitting class construction is presented which has affinities with that of \textit{R. S. Dark} [Math. Z. 127, 145-156 (1972; Zbl 0226.20013)]. All groups considered are finite and soluble. Let \(p\), \(q\), \(r\) be primes. The author defines \({\mathcal M}\) as the class of groups of the form \(ABU\), where \(A\), \(B\) and \(U\) are nontrivial ...
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Subdirect product closed fitting classes
1974In [2] we pointed out that the class of finite soluble groups whose socle is central is an R 0-closed Fitting class. It follows that if p, q are primes, the class S p S q contains a proper, non-nilpotent, R 0-closed Fitting class. This contrasts with the closure operations S, E o and, when q|p−1, Q — see [2] for details and notation.
R. A. Bryce, John Cossey
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Subgroup closed Fitting classes
Mathematical Proceedings of the Cambridge Philosophical Society, 1978In (1) we showed that a subgroup closed Fitting formation is a primitive saturated formation, and in (2) we showed that a subgroup closed and metanilpotent Fitting class is a formation. Whether or not a subgroup closed Fitting class is always a formation is a question that has plagued us ever since.
Bryce, R. A., Cossey, John
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Lattices of partially local fitting classes
Siberian Mathematical Journal, 2009Summary: This article deals only with finite groups. We prove the surjectivity of the mapping from the lattice of all normal Fitting classes into the lattice of the Lockett section generated by the Fitting classes that are not Lockett classes. Moreover, we find a sufficient surjectivity condition for the mapping of the lattice of the Lockett section ...
Zalesskaya, E. N., Vorob’еv, N. N.
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Journal of Algebra, 2020
Abstract Let σ be a partition of the set of all primes P . If G is a finite group and F is a Fitting class of finite groups, the symbol σ ( G ) denotes the set { σ i | σ i ∩ π ( | G | ) ≠ ∅ } and σ ( F ) = ∪ σ ∈ F σ ( G ) . We call any function f of the form f : σ ⟶ {
Guo, Wenbin, Zhang, Li, Vorob'ev, N.T.
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Abstract Let σ be a partition of the set of all primes P . If G is a finite group and F is a Fitting class of finite groups, the symbol σ ( G ) denotes the set { σ i | σ i ∩ π ( | G | ) ≠ ∅ } and σ ( F ) = ∪ σ ∈ F σ ( G ) . We call any function f of the form f : σ ⟶ {
Guo, Wenbin, Zhang, Li, Vorob'ev, N.T.
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On quasinormal Fitting classes
Communications in AlgebraLet Zp be a group of order p and G≀Zp the regular wreath product of the group G with Zp. A Fitting class F is said to be X -quasinormal if there exists a natural number m such that Gm≀Zp∈F whenever F⊆X , p is a prime, G∈F and G≀Zp∈X . In this paper, we generalize the well known theorem of Blessenohl and Gaschütz and prove that the intersection of ...
Wang, Sizhe +3 more
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