Results 21 to 30 of about 552 (63)
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
On the number of cyclic subgroups of a finite group
, 2018 Let $G$ be a finite group and let $c(G)$ be the number of cyclic subgroups of $G$. We study the function $\alpha(G) = c(G)/|G|$. We explore its basic properties and we point out a connection with the probability of commutation.
Garonzi, Martino, Lima, Igor
core +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 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
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 +2 more
core +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
Approximate groups and doubling metrics
, 2012 We develop a version of Freiman's theorem for a class of non-abelian groups, which includes finite nilpotent, supersolvable and solvable A-groups. To do this we have to replace the small doubling hypothesis with a stronger relative polynomial growth ...
Bray +7 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
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 +2 more
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