Results 1 to 10 of about 5,422,708 (286)
A note on p-solvable and solvable finite groups [PDF]
International Journal of Mathematics and Mathematical Sciences, 1994 The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p-solvable and solvable where p is the largest prime divisor of |G|.
R. Khazal, N. P. Mukherjee
doaj +2 more sources
Diophantine problems in solvable groups [PDF]
Bulletin of Mathematical Sciences, 2020 We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc.), which satisfy some natural “non-commutativity” conditions.
Albert Garreta +2 more
doaj +1 more source
Some criteria for solvability and supersolvability [PDF]
Journal of Mahani Mathematical Research, 2023 Denote by $ G $ a finite group, by $ {\rm hsn}(G) $ the harmonic mean Sylow number (eliminating the Sylow numbers that are one) in $G$ and by $ {\rm gsn}(G) $ the geometric mean Sylow number (eliminating the Sylow numbers that are one) in $G$.
Zohreh Habibi, Masoomeh Hezarjaribi
doaj +1 more source
On a result of nilpotent subgroups of solvable groups [PDF]
International Journal of Group Theory, 2022 Heineken [H. Heineken, Nilpotent subgroups of finite soluble groups, Arch. Math.(Basel), 56 no. 5 (1991) 417--423.] studied the order of the nilpotent subgroups of the largest order of a solvable group.
Yong Yang
doaj +1 more source
The 3-closure of a solvable permutation group is solvable [PDF]
Journal of Algebra, 2022 Let $m$ be a positive integer and let $Ω$ be a finite set. The $m$-closure of $G\leq\operatorname{Sym}(Ω)$ is the largest permutation group on $Ω$ having the same orbits as $G$ in its induced action on the Cartesian product $Ω^m$. The $1$-closure and $2$-closure of a solvable permutation group need not be solvable.
E.A. O'Brien +3 more
openaire +2 more sources
Irredundant families of maximal subgroups of finite solvable groups [PDF]
International Journal of Group Theory, 2023 Let $\mathcal{M}$ be a family of maximal subgroups of a group $G.$ We say that $\mathcal{M}$ is irredundant if its intersection is not equal to the intersection of any proper subfamily of $\mathcal{M}$. The maximal dimension of $G$ is the maximal size of
Agnieszka Stocka
doaj +1 more source
Partition numbers of finite solvable groups [PDF]
Advances in Group Theory and Applications, 2018 A group partition is a group cover in which the elements have trivial pairwise intersection. Here we define the partition number of a group - the minimal number of subgroups necessary to form a partition - and examine some of its properties, including ...
Tuval Foguel, Nick Sizemore
doaj +1 more source
The codegrees of real-valued Irreducible characters of finite groups [PDF]
ریاضی و جامعه, 2023 In this note we show that if every codegree of real-valued irreducible characters of a finite group $G$ is either a $2$-number or $2'$-number, then $G$ is ...
Zeynab Akhlaghi
doaj +1 more source
Solvable groups whose monomial, monolithic characters have prime power codegrees [PDF]
International Journal of Group Theory, 2023 In this note, we prove that if $G$ is solvable and ${\rm cod}(\chi)$ is a $p$-power for every nonlinear, monomial, monolithic $\chi\in {\rm Irr}(G)$ or every nonlinear, monomial, monolithic $\chi \in {\rm IBr} (G)$, then $P$ is normal in $G$, where $p ...
Xiaoyou Chen, Mark Lewis
doaj +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