Results 31 to 40 of about 5,389,809 (116)

Maximal subgroups of finite groups

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 2, Page 311-314, 1990., 1989
In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting ...
S. Srinivasan
wiley   +1 more source

A survey of the number of supersolvable subgroups of finite groups

, 2022
In this paper we survey a new criteria for solvability of finite groups in terms of number of supersolvable (also known as polycyclic) and non-supersolvable subgroups.
Acosta-Humánez, Primitivo B., Liriano, Orieta, Mora-Ferreras, Francis   +2 more
core  

On stabilizers in finite permutation groups

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract Let G$G$ be a permutation group on the finite set Ω$\Omega$. We prove various results about partitions of Ω$\Omega$ whose stabilizers have good properties. In particular, in every solvable permutation group there is a set‐stabilizer whose orbits have length at most 6, which is best possible and answers two questions of Babai.
Luca Sabatini
wiley   +1 more source

A note on finite group structure influenced by second and third maximal subgroups

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 747-750, 1990., 1990
The structure of a finite group having specified number of second and third maximal subgroups has been investigated in the paper.
N. P. Mukherjee, R. Khazal
wiley   +1 more source

Equivariant Hilbert and Ehrhart series under translative group actions

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study representations of finite groups on Stanley–Reisner rings of simplicial complexes and on lattice points in lattice polytopes. The framework of translative group actions allows us to use the theory of proper colorings of simplicial complexes without requiring an explicit coloring to be given.
Alessio D'Alì, Emanuele Delucchi
wiley   +1 more source

A generalized Frattini subgroup of a finite group

International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 2, Page 263-266, 1989., 1989
For a finite group G and an arbitrary prime p, let SP(G) denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set SP(G) = G. Some properties of G are considered involving SP(G).
Prabir Bhattacharya, N. P. Mukherjee
wiley   +1 more source

A Jordan–Chevalley decomposition beyond algebraic groups

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract We prove a decomposition of definable groups in o‐minimal structures generalizing the Jordan–Chevalley decomposition of linear algebraic groups. It follows that any definable linear group G$G$ is a semidirect product of its maximal normal definable torsion‐free subgroup N(G)$\mathcal {N}(G)$ and a definable subgroup P$P$, unique up to ...
Annalisa Conversano
wiley   +1 more source

A note on influence of subgroup restrictions in finite group structure

International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 4, Page 721-724, 1989., 1988
The structure of a finite group under specific restrictions respectively on its maximal, minimal and prime power subgroups has been investigated in this paper.
R. Khazal, N. P. Mukherjee
wiley   +1 more source

On finite d$d$‐maximal groups

Bulletin of the London Mathematical Society, Volume 56, Issue 3, Page 1054-1070, March 2024.
Abstract Let d$d$ be a positive integer. A finite group is called d$d$‐maximal if it can be generated by precisely d$d$ elements, whereas its proper subgroups have smaller generating sets. For d∈{1,2}$d\in \lbrace 1,2\rbrace$, the d$d$‐maximal groups have been classified up to isomorphism and only partial results have been proved for larger d$d$.
Andrea Lucchini, Luca Sabatini, Mima Stanojkovski   +2 more
wiley   +1 more source

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