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Fitting Classes with Given Properties of Hall Subgroups [PDF]
Mathematical Notes, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zagurskii, V. N., Vorob’ev, N. T.
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On locally normal Fitting classes of finite soluble groups
Journal of Algebra, 2003 Let X,F,X⊆F, be non-trivial Fitting classes of finite soluble groups such that GX is an X-injector of G for all G∈F. Then X is said to be normal in F (F-normal).
Reifferscheid, Stephanie
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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 Lockett conjecture for σ-local Fitting classes
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022All groups appearing in this review will be finite. A class of groups \(\mathcal F\) is called a Fitting class if it is closed under normal subgroups and products of normal \(\mathcal F\)-subgroups. It is well known that many problems related to Fitting classes can be studied by using the operators \(``^{*}"\) and \(``_{*}"\) defined by \textit{F.
Vorob'ev, N. T., Volkova, E. D.
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On the distributivity of the lattice of solvable totally local fitting classes [PDF]
Mathematical Notes, 2000 It is proved that the lattice of all solvable totally local Fitting classes is algebraic and ...
N N Vorob'Ev +2 more
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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 any ...
Wang, Sizhe +3 more
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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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Rendiconti del Circolo Matematico di Palermo, 1999
Let \(\mathcal X\) be a homomorph and let \(G\) be a finite group. A chief factor \(F\) of group \(G\) is an \(\mathcal X\)-chief factor of \(G\) if \(F\in{\mathcal X}\). It is denoted by \(C_{\mathcal X}(G)=\bigcap\{C_G(F)\mid F\) is an \(\mathcal X\)-chief factor of \(G\}\) if the set of \(\mathcal X\)-chief factors of \(G\) is nonempty, otherwise ...
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Let \(\mathcal X\) be a homomorph and let \(G\) be a finite group. A chief factor \(F\) of group \(G\) is an \(\mathcal X\)-chief factor of \(G\) if \(F\in{\mathcal X}\). It is denoted by \(C_{\mathcal X}(G)=\bigcap\{C_G(F)\mid F\) is an \(\mathcal X\)-chief factor of \(G\}\) if the set of \(\mathcal X\)-chief factors of \(G\) is nonempty, otherwise ...
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Mathematical Proceedings of the Cambridge Philosophical Society, 1976
This note is devoted to the construction of a 〈Q, EΦ〉-closed Fischer class which is not a formation. It provides a negative answer to the Questions 3–7 raised by Cossey in (1). All groups considered are finite and soluble.
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This note is devoted to the construction of a 〈Q, EΦ〉-closed Fischer class which is not a formation. It provides a negative answer to the Questions 3–7 raised by Cossey in (1). All groups considered are finite and soluble.
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Formations and Fitting Classes
2015In Chapter V, we introduce the relevant knowledge for formation and Fitting class, and describe some of their related new results including the basic theory of part composition and partial local formations, factorization of formations and their lattice structure, the canonical subgroups related to formations and Fitting classes, the theory of ...
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