Results 241 to 250 of about 798,154 (283)

On nilpotent subgroups containing non-trivial normal subgroups

Journal of Group Theory, 2010
Let \(G\) be a non-trivial finite group and let \(A\) be a nilpotent subgroup of \(G\). The author proves that if \(|G:A|\leq\exp(A)\), the exponent of \(A\), then \(A\) contains a non-trivial normal subgroup of \(G\). This extends an earlier result by \textit{I. M. Isaacs} [Proc. Am. Math. Soc. 130, No. 7, 1923-1925 (2002; Zbl 0993.20001)], who proved
Jamali, A. R., Viseh, M.
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Normality for elementary subgroup functors

Mathematical Proceedings of the Cambridge Philosophical Society, 1995
AbstractWe define a notion of group functor G on categories of graded modules, which unifies previous concepts of a group functor G possessing a notion of elementary subfunctor E. We show under a general condition which is easily checked in practice that the elementary subgroup E(M) of G(M) is normal for all quasi-weak Noetherian objects M in the ...
Bak, Anthony, Vavilov, N.
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Solvable subgroups in groups with self-normalizing subgroup

Ukrainian Mathematical Journal, 2008
Summary: We study the structure of some solvable finite subgroups in groups with self-normalizing subgroup.
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NORMAL SUBGROUPS OF FUCHSIAN GROUPS

The Quarterly Journal of Mathematics, 1985
It is well-known that all finitely-generated Fuchsian groups contain torsion-free normal subgroups of finite index and the particular case of the (2,3,7)-triangle group has been much studied as the corresponding quotient groups are maximal groups of automorphisms of compact Riemann surfaces.
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On subgroups containing non-trivial normal subgroups

Israel Journal of Mathematics, 2003
We prove that ifA≠1 is a subgroup of a finite groupG and the order of an element in the centralizer ofA inG is strictly larger (larger or equal) than the index [G:A], thenA contains a non-trivial characteristic (normal) subgroup ofG. Consequently, ifA is a stabilizer in a transitive permutation group of degreem>1, thenexp(Z(A))
HERZOG M., KAPLAN G., LUCCHINI, ANDREA
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Groups with Supersoluble Non-normal Subgroups

Algebra Colloquium, 2016
The structure of groups in which many subgroups have a certain property χ has been investigated for several choices of the property χ. In particular, groups whose non-normal subgroups are supersoluble are studied in this paper. Moreover, groups with only finitely many normalizers of non-supersoluble groups are considered.
DE FALCO, MARIA, MARTUSCIELLO, MARIA, MUSELLA, CARMELA   +2 more
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NORMAL SUBGROUPS OF FREE CONSTRUCTIONS

Mathematics of the USSR-Sbornik, 1986
Let \({\mathcal G}\) be the smallest class of groups with the following properties: 1) \({\mathcal G}\) contains all cyclic groups, 2) \({\mathcal G}\) is closed with respect to the second order operations in a finite or countable number - taking HNN-extensions with free or cyclic associated subgroups or taking amalgamated free products with free or ...
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Normal nearness subgroups

Communications in Algebra, 2023
Mehmet Ali Öztürk, Özlem Tekin, Young Bae Jun   +2 more
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On Normal Embedding of Subgroups

Geometriae Dedicata, 2000
The author surveys conditions for a group to allow an embedding as a normal subgroup of another finite group, with an additional condition of containment in some given characteristic subgroup. The main objects of the article are finite groups. Let \(\Aut_c(G)\) denote the group of all central automorphisms of a group \(G\), \(\text{Inn}_c(G)=\Aut_c(G ...
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Normal Subgroups

2017
Claudia Menini, Freddy Van Oystaeyen
openaire   +1 more source