Results 31 to 40 of about 80 (76)

Some results on π‐solvable and supersolvable groups [PDF]

International Journal of Mathematics and Mathematical Sciences, 1993
For a finite group G, ϕp(G), Sp(G), L(G) and S𝒫(G) are generalizations of the Frattini subgroup of G. We obtain some results on π‐solvable, p‐solvable and supersolvable groups with the help of the structures of these subgroups.
T. K. Dutta, A. Bhattacharyya
openaire   +3 more sources

Inductive and divisional posets

Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.
Abstract We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we introduce and study the notion of inductive posets and their superclass of divisional posets.
Roberto Pagaria, Maddalena Pismataro, Tan Nhat Tran, Lorenzo Vecchi   +3 more
wiley   +1 more source

$G$-permutable Subgroups in $\operatorname{PSL}_2(q)$ and Hereditarily $G$-permutable Subgroups in $\operatorname{PSU}_3(q)$

Известия Иркутского государственного университета: Серия "Математика"
The concept of $X$-permutable subgroup, introduced by A. N. Skiba, generalizes the classical concept of a permutable subgroup. Many classes of finite groups have been characterized in terms of $X$-permutable subgroups.
A. A. Galt, V. N. Tyutyanov
doaj   +1 more source

Two-closures of supersolvable permutation groups in polynomial time [PDF]

computational complexity, 2020
The $2$-closure $\overline{G}$ of a permutation group $G$ on $Ω$ is defined to be the largest permutation group on $Ω$, having the same orbits on $Ω\timesΩ$ as $G$. It is proved that if $G$ is supersolvable, then $\overline{G}$ can be found in polynomial time in $|Ω|$.
Ponomarenko, Ilia, Vasil'ev, Andrey
openaire   +2 more sources

Large Orbits of Supersolvable Linear Groups

Journal of Algebra, 1999
The study of regular orbits of linear groups plays an important role in representation theory, particularly that of solvable groups because a chief factor of a solvable group \(G\) is an irreducible \(G\)-module. Existence of regular orbits has had applications to Brauer's conjectures on height zero characters and block size as well as length-type ...
openaire   +1 more source

Finite group with some c#-normal and S-quasinormally embedded subgroups

Open Mathematics
Let pp be a prime that divides the order of a finite group GG, and let PP be a Sylow pp-subgroup of GG. Assume that dd is the smallest number of generators of PP and define ℳd(P)={P1,P2,…,Pd}{{\mathcal{ {\mathcal M} }}}_{d}\left(P)=\left\{{P}_{1},{P}_{2},
Li Ning, Jiang Jing, Liu Jianjun
doaj   +1 more source

p-supersolvability of factorized finite groups

Hokkaido Mathematical Journal, 1992
The author calls two subgroups \(H\), \(K\) of a group mutually permutable if \(H\) is permutable with every subgroup of \(K\) and \(K\) is permutable with every subgroup of \(H\). He obtains the following main results: If \(G = HK \neq 1\) and \(H\) and \(K\) are mutually permutable, then \(H\) or \(K\) contains a nontrivial normal subgroup of \(G ...
openaire   +3 more sources

SR-groups of Order 2ⁿp^m with Dihedral Sylow 2-subgroup

Моделирование и анализ информационных систем, 2007
The structure of SR-groups with dihedral Sylow 2-subgroup modulo Frattini subgroup is described. It is proved that if a group О is a non-supersolvable SR-group of order 2npm with dihedral Sylow 2-subgroup, p is Mersenne prime.
V. V. Yanishevskiy
doaj  

Finite Minimal Non-$ \sigma $-Supersolvable Groups

Siberian Mathematical Journal
Abstract Let $ \sigma $ be a partition of the set of all primes. A finite group $ G $ is said to be $ \sigma $ -supersolvable if every $ G $ -chief factor of its $ \sigma $ -nilpotent residual is cyclic ...
openaire   +1 more source

Minimal non-nilpotent groups which are supersolvable

, 2009
The structure of a group which is not nilpotent but all of whose proper subgroups are nilpotent has interested the researches of several authors both in the finite case and in the infinite case. The present paper generalizes some classic descriptions of M. Newman, H. Smith and J. Wiegold in the context of supersolvable groups.
openaire   +3 more sources