Results 211 to 220 of about 10,264,920 (253)
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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 the injectors of finite groups
Journal of Group Theory, 2007All groups considered in the paper are finite. Let \(\pi\) be a set of primes and let \(\mathfrak F\) be a non-empty Fitting class. We denote by \(E^{\mathfrak N}_\pi\) the class of groups \(G\) such that \(G\) contains a nilpotent Hall \(\pi\)-subgroup.
Guo, Wenbin, Li, Baojun
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Mathematische Nachrichten, 1993
AbstractThe structure of the finite Krutik‐groups is investigated. It is shown that they are solvable groups with very special properties.
Brandl, R., Deaconescu, M.
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AbstractThe structure of the finite Krutik‐groups is investigated. It is shown that they are solvable groups with very special properties.
Brandl, R., Deaconescu, M.
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On the solvability of finite groups
Archiv der Mathematik, 1988In earlier papers the author has shown that normality of certain subgroups insures solvability or supersolvability. In this paper he shows that normality can be replaced by quasinormality. Let G be a finite group and define \(A_ 1=\{H\leq G:\) H has prime order or is cyclic of order \(4\}\), \(A_ 2=\{H\leq G:\) H has order 2p, p an odd prime\(\}\) and \
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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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On the diameter of finite groups
Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, 2002The diameter of a group G with respect to a set S of generators is the maximum over g in G of the length of the shortest word in S union S/sup -1/ representing g. This concept arises in the contexts of efficient communication networks and Rubik's-cube-type puzzles.
László Babai +4 more
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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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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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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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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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