Results 281 to 290 of about 151,917 (318)
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Algebra Colloquium, 2007
The norm N(G) of a group G is the intersection of normalizers of all the subgroups of G. Let G be a finite group, p a prime dividing the order of G, and P a Sylow p-subgroup of G. In this paper, it is proved that G is p-nilpotent if Ω1(P) ≤ N(NG(P)), and when p=2, [Formula: see text]. Some applications of this result are given.
Wang, Junxin, Guo, Xiuyun
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The norm N(G) of a group G is the intersection of normalizers of all the subgroups of G. Let G be a finite group, p a prime dividing the order of G, and P a Sylow p-subgroup of G. In this paper, it is proved that G is p-nilpotent if Ω1(P) ≤ N(NG(P)), and when p=2, [Formula: see text]. Some applications of this result are given.
Wang, Junxin, Guo, Xiuyun
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ON AUTOMORPHISMS OF FINITE GROUPS
Mathematics of the USSR-Sbornik, 1974We consider orbits of elements of a finite group G with respect to the action on G of a cyclic automorphism group generated by . We obtain sufficient conditions for the existence of an orbit whose length is equal to the order of the automorphism . Namely, such an orbit exists for any automorphism of a semisimple or nilpotent finite group G and for an ...
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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.
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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.
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Journal of Mathematical Sciences, 1998
The present survey is based mainly on papers presented over the years 1983-1992 and can be considered as a continuation of the corresponding sections of the surveys ``Finite groups'' published in the years 1966, 1971, 1976 and 1986 by different authors (1966; Zbl 0207.33302, 1971; Zbl 0224.20006, 1976; Zbl 0444.20011, 1986; Zbl 0632.20009).
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The present survey is based mainly on papers presented over the years 1983-1992 and can be considered as a continuation of the corresponding sections of the surveys ``Finite groups'' published in the years 1966, 1971, 1976 and 1986 by different authors (1966; Zbl 0207.33302, 1971; Zbl 0224.20006, 1976; Zbl 0444.20011, 1986; Zbl 0632.20009).
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Journal of the London Mathematical Society, 2000
A group is called homogeneous if any isomorphism between two finitely generated subgroups is induced by some automorphism. In [J. Lond. Math. Soc., II. Ser. 44, No. 1, 102-120 (1991; Zbl 0789.20033)] the authors classified homogeneous finite solvable groups.
Cherlin, Gregory, Felgner, Ulrich
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A group is called homogeneous if any isomorphism between two finitely generated subgroups is induced by some automorphism. In [J. Lond. Math. Soc., II. Ser. 44, No. 1, 102-120 (1991; Zbl 0789.20033)] the authors classified homogeneous finite solvable groups.
Cherlin, Gregory, Felgner, Ulrich
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On the Characters of Finite Groups
The Annals of Mathematics, 1955where each A is an irreducible character of some elementary subgroup (si of (M, ip* designates the character of (M induced by AXv , and where the ai belong to the ring Z of rational integers. Here, an elementary group is defined as a group which is the direct product of a cyclic group and a p-group for some prime number p. By a generalized character of
Brauer, Richard, Tate, John
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Siberian Mathematical Journal, 2007
Summary: We study the so-called finite tangled groups. These are the groups in which every subset containing 1 and closed under the operation \(x\circ y=xy^{-1}x\) is a subgroup. The general problem of studying such groups reduces to the case of tangled groups of odd order. We classify all finite nilpotent tangled groups.
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Summary: We study the so-called finite tangled groups. These are the groups in which every subset containing 1 and closed under the operation \(x\circ y=xy^{-1}x\) is a subgroup. The general problem of studying such groups reduces to the case of tangled groups of odd order. We classify all finite nilpotent tangled groups.
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Algebra universalis, 2005
Let \(G\) and \(H\) be groups such that the subgroup lattices of \(G^3=G\times G\times G\) and \(H^3=H\times H\times H\) are isomorphic. The question whether then \(G\) and \(H\) are isomorphic has been answered, in the negative, by the authors [J. Group Theory 7, No. 3, 385-402 (2004; Zbl 1071.20028)].
Kearnes, Keith A., Szendrei, Ágnes
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Let \(G\) and \(H\) be groups such that the subgroup lattices of \(G^3=G\times G\times G\) and \(H^3=H\times H\times H\) are isomorphic. The question whether then \(G\) and \(H\) are isomorphic has been answered, in the negative, by the authors [J. Group Theory 7, No. 3, 385-402 (2004; Zbl 1071.20028)].
Kearnes, Keith A., Szendrei, Ágnes
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On commutators in finite groups
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1953$R$ sei der von den Klassen konjugierte Elemente der endlichen Gruppe $G$ erzeugte Ring. Verf. beweist: 1) Notwendige und hinreichende Bedingung dafür, daß ein Element $a\in G$ Kommutator in $G$ sei, ist: In der regulären Darstellung von $R$ muß die Klasse $\langle a\rangle$ von $a$ einen von $0$ verschiedenen Charakter haben.
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Mathematics of the USSR-Izvestiya, 1968
The immersion of normal subgroups in a solvable (or partially solvable) finite group is studied. In a series of cases the results obtained are presented in the form of a connection between a group and its group of operators.
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The immersion of normal subgroups in a solvable (or partially solvable) finite group is studied. In a series of cases the results obtained are presented in the form of a connection between a group and its group of operators.
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