Results 21 to 30 of about 250,418 (87)

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 non-solvable groups with given number of particular subgroups

Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science
Considering the quantitative properties of some particular subgroups of a finite group, we prove that (1) a non-solvable group $G$ has exactly 5 non-subnormal non-supersolvable proper subgroups if and only if $G\cong A_5$ or $SL_2(5)$. (2) a non-solvable
Jiangtao Shi, Fanjie Xu, Yifan Liu
semanticscholar   +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

A Frobenius-type theorem for supersolvable groups

Publicationes mathematicae (Debrecen), 1996
Frobenius’ Theorem for p-nilpotent groups is one of the most fundamental theorems in finite group theory. In this paper a Frobenius-type Theorem for supersolvable groups is given by applying strictly p-closed groups, and some applications are obtained ...
Wang Caiyun, Guo Xiuyun
semanticscholar   +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

On the homotopy Lie algebra of an arrangement

, 2005
Let A be a graded-commutative, connected k-algebra generated in degree 1. The homotopy Lie algebra g_A is defined to be the Lie algebra of primitives of the Yoneda algebra, Ext_A(k,k). Under certain homological assumptions on A and its quadratic closure,
Denham, Graham, Suciu, Alexander I.
core   +3 more sources

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

$G$-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

The first Hochschild cohomology as a Lie algebra

, 2019
In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic.
Degrassi, Lleonard Rubio y, Schroll, Sibylle, Solotar, Andrea   +2 more
core   +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