Results 31 to 40 of about 2,137 (216)
On numbers which are orders of nilpotent groups with bounded class [PDF]
International Journal of Group TheoryLet $n$ be a positive integer. In this short note, we characterize those numbers $m$ for which any group of order $m$ is an $n$-Engel group and those numbers $m$ for which any group of order $m$ has all its subgroups subnormal of defect at most $n$.
Maria Ferrara
doaj +1 more source
Finite groups with semi-subnormal Schmidt subgroups
, 2020 A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup A of a group G is semi-normal in G if there exists a subgroup B of G such that G = AB and AB1 is a proper subgroup of G for every proper subgroup B1 of B. If
Monakhov, V.S., Kniahina, V.N.
core +1 more source
On Subnormal Subgroups of Factorized Groups
Journal of Algebra, 1997 Let the group \(G=AB\) be the product of two subgroups \(A\) and \(B\), and let \(H\) be a subgroup of the intersection \(A\cap B\). A well-known result of Maier and Wielandt says that if \(G\) is finite and the subgroup \(H\) is subnormal in \(A\) and \(B\), then \(H\) is also subnormal in \(G\) [see the book ``Products of groups'', Oxford Univ. Press
DE GIOVANNI, FRANCESCO +2 more
openaire +2 more sources
Subnormal Structure of Finite Soluble Groups [PDF]
, 2001 The Wielandt subgroup, the intersection of normalizers of subnormal subgroups, is non-trivial in any finite group and thus gives rise to a series whose length is a measure of the complexity of a group's subnormal structure.
Wetherell, Chris
core +1 more source
Finite groups in which normality, permutability or Sylow permutability is transitive
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 Y. Li gave a characterization of the class of finite soluble groups in which every subnormal subgroup is normal by means of NE-subgroups: a subgroup H of a group G is called an NE-subgroup of G if NG(H) ∩ HG = H. We obtain a new characterization of these
Malinowska Izabela Agata
doaj +1 more source
On the Finite Group Which Is a Product of Two Subnormal Supersolvable Subgroups
Mathematics, 2022 Let G be a finite group that is a product of two subnormal ( normal) supersolvable subgroups. The following are interesting topics in the study of the structure of G: obtaining the conditions in addition to guarantee that G is supersolvable and giving ...
Yangming Li, Yubo Lv, Xiangyang Xu
doaj +1 more source
Joins of Almost Subnormal Subgroups [PDF]
Proceedings of the Edinburgh Mathematical Society, 1979 Following (1) we say that a subgroup H of a group G is almost subnormal in G if H is of finite index in some subnormal subgroup of G, or, equivalently, if |Hn : H| is finite for some n, where Hn is the n-th term of the normal closure series of H in G. The aim of this article is to prove, in answer to a question of R. Baer, the following analogue of the
openaire +1 more source
Finite groups whose maximal subgroups of even order are MSN-groups
Open Mathematics, 2022 A finite group GG is called an MSN-group if all maximal subgroups of the Sylow subgroups of GG are subnormal in GG. In this article, we investigate the structure of finite groups GG such that GG is a non-MSN-group of even order in which every maximal ...
Wang Wanlin, Guo Pengfei
doaj +1 more source
A Survey of Subnormal Subgroups
Irish Mathematical Society Bulletin, 1990 The author gives a survey (without proofs) of the high points of the theory of subnormal subgroups developed over the last fifty years. The article is intended as an introduction to the book by Lennox and Stonehewer.
openaire +2 more sources
International Journal of Mathematics and Mathematical Sciences, 1997 Let G be a finite group and H be an operator group of G. In this short note, we show a relationship between subnormal subgroup chains and H-invariant subgroup chains.
Yanming Wang
doaj +1 more source