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Finite Groups with Weakly Subnormal and Partially Subnormal Subgroups

Siberian Mathematical Journal, 2021
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Alexander N Skiba, Hu B, Skiba A N
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GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS

Bulletin of the Australian Mathematical Society, 2012
AbstractWe 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, 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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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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Subnormal Subgroups of Division Rings

Canadian Journal of Mathematics, 1963
Let K be a division ring. A subgroup H of the multiplicative group K′ of K is subnormal if there is a finite sequence (H = A0, A1, . . . , An = K′) of subgroups of K′ such that each Ai is a normal subgroup of Ai+1. It is known (2, 3) that if H is a subdivision ring of K such that H′ is subnormal in K′, then either H = K or H is in the centre Z(K) of K.
Herstein, I. N., Scott, W. R.
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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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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, Monakhov V S
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On subnormal subgroups of linear groups

Siberian Mathematical Journal, 2008
Summary: We describe the subnormal subgroups of 2-dimensional linear groups over local and full rings in which 2 is invertible, as well as the subnormal subgroups of symplectic groups over local rings in which 2 is invertible.
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On cofactors of subnormal subgroups

Journal of Algebra and Its Applications, 2016
For a soluble finite group [Formula: see text] and a prime [Formula: see text] we let [Formula: see text], [Formula: see text]. We obtain upper bounds for the rank, the nilpotent length, the derived length, and the [Formula: see text]-length of a finite soluble group [Formula: see text] in terms of [Formula: see text] and [Formula: see text].
Monakhov, Victor, Sokhor, Irina
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Maximal Subgroups of Almost Subnormal Subgroups in Division Rings

Acta Mathematica Vietnamica, 2021
A subgroup \(H\) of \(G\) is called ``almost subnormal'' if there exists a finite sequence of subgroups \(H=H_1 < H_2 < \dots
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