Results 221 to 230 of about 180,475 (263)
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Maximal subclasses of local fitting classes
Siberian Mathematical Journal, 2008Summary: A Fitting class \(\mathfrak F\) is said to be \(\pi\)-maximal if \(\mathfrak F\) is an inclusion maximal subclass of the Fitting class \(\mathfrak S_\pi\) of all finite soluble \(\pi\)-groups. We prove that \(\mathfrak F\) is a \(\pi\)-maximal Fitting class exactly when there is a prime \(p\in\pi\) such that the index of the \(\mathfrak F ...
Savelyeva, N. V., 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 any ...
Wang, Sizhe +3 more
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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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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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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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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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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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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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