Results 191 to 200 of about 581,922 (233)

NILPOTENT SUBGROUPS OF GROUPS WITH ALL SUBGROUPS SUBNORMAL

Bulletin of the London Mathematical Society, 2003
The 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.
openaire   +2 more sources

On division subrings normalized by almost subnormal subgroups in division rings

Periodica Mathematica Hungarica, 2018
Let D be a division ring with infinite center, K a proper division subring of D and N an almost subnormal subgroup of the multiplicative group $$D^*$$ D ∗ of D .
T. T. Deo, M. H. Bien, B. X. Hai
semanticscholar   +2 more sources

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.
openaire   +2 more sources

Groups with subnormal or modular Schmidt 𝑝𝑑-subgroups

Journal of group theroy
A Schmidt group is a finite non-nilpotent group such that every proper subgroup is nilpotent. In this paper, we prove that if every Schmidt subgroup of a finite group 𝐺 is subnormal or modular, then G / F ⁢ ( G ) G/F(G) is cyclic.
V. Monakhov, I. Sokhor
semanticscholar   +1 more source

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
openaire   +3 more sources

Finite groups with given sets of 𝔉-subnormal subgroups

Asian-European Journal of Mathematics, 2018
In this paper, the classes of groups with given systems of [Formula: see text]-subnormal subgroups are studied. In particular, it is showed that if [Formula: see text] and [Formula: see text] are a saturated homomorph and a hereditary saturated formation,
V. I. Murashka
semanticscholar   +1 more source

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.
openaire   +1 more source

Hypercentral Groups with all Subgroups Subnormal II

Bulletin of the London Mathematical Society, 1986
It is shown that a hypercentral group that has all subgroups subnormal and every non-nilpotent subgroup of bounded defect is nilpotent. As a consequence, a hypercentral group of length at most ω in which every subgroup is subnormal is nilpotent.
openaire   +3 more sources

On Groups with all Subgroups Subnormal

Bulletin of the London Mathematical Society, 1985
It 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.
openaire   +1 more source

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
openaire   +2 more sources