Results 41 to 50 of about 1,123 (133)

Mutually Permutable Products of Finite Groups

International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011
Let G be a finite group and G1, G2 are two subgroups of G. We say that G1 and G2 are mutually permutable if G1 is permutable with every subgroup of G2 and G2 is permutable with every subgroup of G1. We prove that if G = G1G2 = G1G3 = G2G3 is the product of three supersolvable subgroups G1, G2, and G3, where Gi and Gj are mutually permutable for all i ...
Rola A. Hijazi, M. Asaad, G. Buskes, G. Mason, L. Vinet   +4 more
wiley   +1 more source

A note on p‐solvable and solvable finite groups

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 821-824, 1994., 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|. These are used further in identifying the largest normal p‐solvable and normal solvable subgroups, respectively, of G.
R. Khazal, N. P. Mukherjee
wiley   +1 more source

Supersolvable Q-Groups

, 2012
One important problem in Q-gruops theory is to classify particular dasses of Q-groups.
Ion Armeanu
openalex   +2 more sources

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 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