Results 1 to 10 of about 44 (42)
Metahamiltonian groups and related topics [PDF]
International Journal of Group Theory, 2013 A group is called metahamiltonian if all its non-abelian subgroups are normal. This aim of this paper is to provide an updated survey of researches concerning certain classes of generalized metahamiltonian groups, in various contexts, and to prove some ...
Maria De Falco +2 more
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On the Structure of Groups whose Non-Abelian Subgroups are Serial [PDF]
Advances in Group Theory and Applications, 2016 Necessary and sufficient conditions are given for a locally finite group to have all non-abelian subgroups serial. We also obtain results for groups whose non-abelian subgroups are permutable.
M.R. Dixon, L.A. Kurdachenko, N.N. Semko
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A Classification of Finite Metahamiltonian p-Groups [PDF]
Communications in Mathematics and Statistics, 2021 A finite non-abelian group \(G\) is called metahamiltonian if every subgroup of \(G\) is either abelian or normal in \(G\). If every subgroup of \(G\) is normal in \(G\), then \(G\) is called Hamiltonian and such groups were classified by \textit{R. Dedekind} [Math. Ann. 48, 548--561 (1897; JFM 28.0129.03)]. If every proper subgroup of \(G\) is abelian,
Xingui Fang, Lijian An
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Normality in Uncountable Groups [PDF]
Advances in Group Theory and Applications, 2017 The main purpose of this paper is to describe the structure of uncountable groups of cardinality $\aleph$ in which all subgroups of cardinality $\aleph$ are normal.
Maria De Falco +3 more
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Finite metahamiltonian p-groups
Journal of Algebra, 2015 The paper under review contains a series of results about metahamiltonian \(p\)-groups, which are then used by X. G. Fang and the first author to classify these group in a paper in preparation. A non-abelian group is said to be Hamiltonian if all of its subgroups are normal, and metahamiltonian if all of its non-abelian subgroups are normal. The latter
Lijian An, Qinhai Zhang
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On metahamiltonian groups of infinite rank
Journal of Algebra, 2014 A group is metahamiltonian if all its non-Abelian subgroups are normal. The authors continue their research on the influence of the subgroups of infinite rank on the group's structure. In the article, they prove that a generalized soluble group of infinite rank is metahamiltonian if and only if all its subgroups of infinite rank are either Abelian or ...
DE FALCO, MARIA +3 more
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On groups that are nearly metahamiltonian
Researches in Mathematics, 2021 We consider groups whose subgroups are either normal or have Chernikov commutant. It was proved that if such group G has a subgroup H of finite index and its commutant is a Chernikov group, then commutant of group G is a Chernikov group.
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On Finite Metahamiltonian p-Groups
, 2014 arXiv admin note: substantial text overlap with arXiv:1310 ...
An, Lijian, Zhang, Qinhai
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The Classification of Finite Metahamiltonian $p$-Groups
, 2013 A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generation of Hamiltonian groups. In this paper, a complete classification of finite metahamiltonian $p$-groups is given.
Fang, Xingui, An, Lijian
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A note on locally graded minimal non-metahamiltonian groups
TURKISH JOURNAL OF MATHEMATICS, 2017 Summary: We prove that a nonperfect locally graded minimal non-metahamiltonian group \(G\) is a soluble group with derived length of at most 4. On the other hand, if \(G\) is perfect, then \(G/\Phi (G)\) is isomorphic to \(A_{5}\), where \(\Phi (G)\) is the Frattini subgroup of \(G\) and \(A_{5}\) is the alternating group.
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