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Joins of σ-subnormal subgroups

Illinois Journal of Mathematics
26pp
Ferrara M., Trombetti M.
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Finite Groups with Subnormal Schmidt Subgroups

Siberian Mathematical Journal, 2004
A Shmidt group is a finite nonnilpotent group with nilpotent proper subgroups. Given a prime \(p\), a \(pd\)-group is a finite group such that \(p\) divides its order. The authors study the finite groups for which some Shmidt \(pd\)-subgroups are subnormal.
V S Monakhov
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Finite groups with subnormal Schmidt subgroups

Algebra and Logic, 2007
Summary: We give a complete description of the structure of finite non-nilpotent groups all Schmidt subgroups of which are subnormal.
V A Vedernikov
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Groups with many subnormal subgroups [PDF]

Journal of Algebra, 2003
A generalization of groups with all subgroups subnormal is studied. In particular, we prove that a group G with a finite subgroup F such that every subgroup containing F is subnormal of bounded defect, is finite-by-(nilpotent of bounded class) provided ...
Eloisa Detomi
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Subnormality in the join of two subgroups

Journal of Group Theory, 2004
Let \(G=\langle U,V\rangle\) 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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Groups with finitely many normalizers of subnormal subgroups [PDF]

Journal of Algebra, 2006
The structure of soluble groups in which normality is a transitive relation is known. Here, groups with finitely many normalizers of subnormal subgroups are investigated, and the behavior of the Wielandt subgroup of such groups is described; moreover ...
Francesco de Giovanni, Fausto de Mari
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Inductive sources and subnormal subgroups

Archiv der Mathematik, 2004
By 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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On weakly subnormal subgroups which are not subnormal

Archiv der Mathematik, 1987
A 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, 1978
Main 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, 1982
The 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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