Results 1 to 10 of about 254,337 (189)
On σ-Residuals of Subgroups of Finite Soluble Groups
Mathematics, 2023 Let σ={σi:i∈I} be a partition of the set of all prime numbers. A subgroup H of a finite group G is said to be σ-subnormal in G if H can be joined to G by a chain of subgroups H=H0⊆H1⊆⋯⊆Hn=G where, for every j=1,⋯,n, Hj−1 is normal in Hj or Hj/CoreHj(Hj−1)
A. A. Heliel +3 more
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Intersections of prefrattini subgroups in finite soluble groups [PDF]
International Journal of Group Theory, 2017 Let $H$ be a prefrattini subgroup of a soluble finite group $G$. In the paper it is proved that there exist elements $x,y in G$ such that the equality $H cap H^x cap H^y = Phi (G)$ holds.
Sergey Kamornikov
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Journal of the Australian Mathematical Society, 1969 Let p be a class of finite soluble groups which is closed under epimorphic images and let g be a saturated formation. Then if G is a group of minimal order belonging to p but not to g, F(G), the Fitting subgroup of G, is the unique minimal normal subgroup of G. It is to groups with this property that the following proposition is applicable.
J. Ward
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On the σ-Length of Maximal Subgroups of Finite σ-Soluble Groups
Mathematics, 2020 Let σ={σi:i∈I} be a partition of the set P of all prime numbers and let G be a finite group. We say that G is σ-primary if all the prime factors of |G| belong to the same member of σ. G is said to be σ-soluble if every chief factor of G is σ-primary, and
Abd El-Rahman Heliel +2 more
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Generalised norms in finite soluble groups
Journal of Algebra, 2014 Let \(C\) be a class of finite groups, closed with respect to subgroups, quotient groups, and direct products of groups of coprime order. The authors consider the intersection \(K_C(G)\) of all of the normalizers of non-\(C\) subgroups of \(G\) and call it \(C\)-norm. (This is the classical norm for \(C=\{1\}\)).
Ballester-Bolinches, Adolfo +2 more
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Finite soluble groups with metabelian centralizers
Journal of Algebra, 2015 Let \(G\) be a finite solvable group. The authors analyze what can be said about \(G\) when we know that the centralizer in \(G\) of every non-trivial element of \(G\) satisfies some given property. More specifically, they define \(G\) to be in \(CA_d\) if the derived length of the centralizer of every non-identity element of \(G\) is at most \(d\). In
CASOLO, CARLO, Enrico Jabara
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Cover-Avoidance Properties in Finite Soluble Groups [PDF]
Canadian Mathematical Bulletin, 1976 AbstractWe give a general method for constructing subgroups which either cover or avoid each chief factor of the finite soluble group G. A strongly pronorrnal subgroup V, a prefrattini subgroup W, an -normalizer D and intersections and products of V, W, and D axe all constructable.
M. J. Tomkinson
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FINITE AXIOMATIZATION OF FINITE SOLUBLE GROUPS
Journal of the London Mathematical Society, 2006 It is proved that the finite soluble groups can be characterized among finite groups by a first-order sentence, namely, the sentence that asserts that no non-trivial element $g$ is a product of 56 commutators $[x,y]$ with entries $x$, $y$ conjugate to $g$.
John S. Wilson
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Mathematische Zeitschrift, 1968 The author proves two results. Theorem 1. If a Sylow \(p\)-subgroup of a finite \(p\)-soluble group \(G\) can be generated by \(d\) elements, then the \(p\)-length of \(G\) is at most \(d\). Theorem 2. If each Sylow subgroup of a finite soluble group \(G\) can be generated by \(d\) elements, then \(G\) can be generated by \(d+1\) elements.
L. Kovács
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Restrictions on sets of conjugacy class sizes in arithmetic progressions [PDF]
International Journal of Group Theory, 2023 We continue the investigation, that began in [M. Bianchi, A. Gillio and P. P. Pálfy, A note on finite groups in which the conjugacy class sizes form an arithmetic progression, Ischia group theory 2010, World Sci. Publ., Hackensack, NJ (2012) 20--25.] and
Alan R. Camina, Rachel D. Camina
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