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On σ-Subnormal Subgroups of Finite Groups
Siberian Mathematical Journal, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S F Kamornikov, V N Tyutyanov
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A Note on Subnormal Subgroups of Division Algebras
Canadian Journal of Mathematics, 1978 Let D be a division algebra and let D* denote the multiplicative group of nonzero elements of D. In [3] Herstein and Scott asked whether any subnormal subgroup of D* must be normal in D*.
Gary R. Greenfield
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Groups in which every subgroup is f-subnormal
Journal of Group Theory, 2001 A subgroup $H$ of a group $G$ is called $f$-subnormal in $G$, if there is a finite sequence $H=H_0\le H_1\le\cdots\le H_k=G$ such that the predecessor is normal in the following term whenever the index is infinite.
CASOLO C, MAINARDIS, Mario
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GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS
Bulletin of the Australian Mathematical Society, 2012AbstractWe consider the class of solvable groups in which all subnormal subgroups have subnormal normalizers, a class containing many well-known classes of solvable groups. Groups of this class have Fitting length three at most; some other information connected with the Fitting series is given.
Beidleman, J. C., Heineken, H.
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Subnormality in the join of two subgroups
Journal of Group Theory, 2004Let \(G=\langle U,V\rangle\) be a group generated by two subgroups \(U\) and \(V\), and let \(H\) be a subgroup of \(U\cap V\) which is subnormal in both \(U\) and \(V\). It is well known that \(H\) need not be subnormal in \(G\), even in the case of finite groups.
CASOLO, CARLO, U. Dardano
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Inductive sources and subnormal subgroups
Archiv der Mathematik, 2004By a character pair in a finite group \(G\) is meant a pair \((H,\theta)\), where \(H\leq G\) and \(\theta\in\text{Irr}(H)\). The group \(G\) acts on the set of character pairs by \((H,\theta)^g=(H^g,\theta^g)\), where \(g\in G\). The character \(\theta^g\) of \(H^g\) is defined by the formula \(\theta^g(h^g)=\theta(h)\) for \(h\in H\).
Isaacs, I. M., Lewis, Mark L.
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Subnormal Subgroups in U( Z G)
Proceedings of the American Mathematical Society, 1988 Let U U be the unit group of the integral group ring of a finite group G G . We prove that every subgroup of U U containing G G and almost subnormal in U U contains ...
Gonçalves, Jairo +2 more
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On weakly subnormal subgroups which are not subnormal
Archiv der Mathematik, 1987A subgroup H of a group G is said to be n-step weakly subnormal in G (written \(H\leq ^ nG)\), for some integer \(n\geq 0\), if there are subsets \(S_ i\) of G such that \(H=S_ 0\subseteq S_ 1\subseteq...\subseteq S_ n=G\) with \(u^{-1}Hu\subseteq S_ i\) for all \(u\in S_{i+1}\), \(0\leq i\leq n-1\). Subnormal subgroups are clearly weakly subnormal and
Maruo, O., Stonehewer, S. E.
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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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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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