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Finite groups with subnormal Schmidt subgroups
Algebra and Logic, 2007Summary: We give a complete description of the structure of finite non-nilpotent groups all Schmidt subgroups of which are subnormal.
V A Vedernikov, Vedernikov V A
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On Certain Properties of Subnormal Subgroups
Canadian Journal of Mathematics, 1978Main results. Let G be a group generated by two subnormal subgroups H and K. Denoting the class of nilpotent groups by 𝔑, and the limit of the lower central series by G𝔑, Wielandt showed in [14], for groups with a composition series ...
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Non-subnormal subgroups of groups
Journal of Pure and Applied Algebra, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Joins of σ-subnormal subgroups
Illinois Journal of Mathematics26pp
Ferrara M., Trombetti M.
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On Groups with all Subgroups Subnormal
Bulletin of the London Mathematical Society, 1985It seems to be unknown whether every group G which has all its subgroups subnormal is soluble. Here it is shown that every such group G in which no nontrivial section is perfect, is hyperabelian and hence (by a result of Brookes) soluble.
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Conditions for subnormality of a join of subnormal subgroups
Mathematical Proceedings of the Cambridge Philosophical Society, 1982The object of this paper is to prove a necessary and sufficient condition on two groups H, K for their join always to be subnormal in a group G whenever they are embedded subnormally in G.
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Coradicals of subnormal subgroups
Algebra and Logic, 1995IfF is a nonempty formation, then theF-coradical of a finite group G is the intersection of all those normal subgroups N of G for which G / N ∈F. We study the structure of theF-coradical of a group generated by two subnormal subgroups of a finite group.
S. F. Kamornikov, L. A. Shemetkov
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NILPOTENT SUBGROUPS OF GROUPS WITH ALL SUBGROUPS SUBNORMAL
Bulletin of the London Mathematical Society, 2003The main result of this remarkable paper is the following theorem: If \(G\) is a group with all subgroups subnormal and \(S\) is a nilpotent subgroup, then the normal closure \(S^G\) is also nilpotent. It follows from here that a group with all subgroups subnormal is a Fitting group (i.e.
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Chains of Normalizers of Subnormal Subgroups
The American Mathematical Monthly, 2022William Cocke +2 more
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On generalised subnormal subgroups of finite groups
Mathematische Nachrichten, 2013AbstractLet \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathfrak {F}}$\end{document} be a formation of finite groups. A subgroup M of a finite group G is said to be \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathfrak {F}}$\end{document}‐normal in G if \documentclass{article ...
Ballester-Bolinches, A. +3 more
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